Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 1 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 1 ỨNG DỤNG ĐẠO HÀM VÀ VẼ ĐỒ THI HÀM SỐ A. LÝ THUYẾT. 1. Định nghĩa: Giả sử K là một khoảng, một đoạn hoặc một nửa khoảng. Hàm số f xác định trên K được gọi là : Hàm số y f x được gọi là đồng biến (tăng) trên K nếu: 1 1 1 2 2 2 . ,, x x x K x x f x f Khi đó, đồ thị của hàm số đi lên từ trái sang phải. Hàm số y f x được gọi là nghịch biến (giảm) trên K nếu: 2 1 2 1 2 1 ,, x x K x x f x f x Khi đó, đồ thị của hàm số đi xuống từ trái sang phải. Hình ảnh minh họa sự đồng biến và nghịch biến của hàm số Đồng biến (tăng) trên K nếu với mọi 1 1 1 2 2 2 . ,, x x x K x x f x f Nghịch biến (giảm) trên K nếu với 2 1 2 1 2 1 ,, x x K x x f x f x . 2. Điều kiện cần để hàm số đơn điệu : Giả sử hàm số f có đạo hàm trên khoảng I Nếu hàm số f đồng biến trên khoảng I thì '0 fx với mọi xI Nếu hàm số f nghịch biến trên khoảng I thì '0 fx với mọi xI 3. Điều kiện đủ để hàm số đơn điệu : 3.1. Định lý : Giả sử I là một khoảng hoặc nửa khoảng hoặc một đoạn, f là hàm số liên tục trên I và có đạo hàm tại mọi điểm trong của I (tức là điểm thuộc I nhưng không phải đầu mút của I ). Khi đó Nếu '0 fx với mọi xI thì hàm số f đồng biến trên khoảng I Nếu '0 fx với mọi xI thì hàm số f nghịch biến trên khoảng I Nếu '0 fx với mọi xI thì hàm số f không đổi trên khoảng I Chú ý : §BÀ I 1. TÍNH ĐƠN ĐI ỆU C ỦA HÀM S Ố Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 2 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Nếu hàm số f liên tục trên ; ab và có đạo hàm '0 fx trên khoảng ; ab thì hàm số f đồng biến trên ; ab Nếu hàm số f liên tục trên ; ab và có đạo hàm '0 fx trên khoảng ; ab thì hàm số f nghịch biến trên ; ab . 3.2. Hệ quả. ta có thể mở rộng định lí trên như sau Giả sử hàm số f có đạo hàm trên khoảng I . Nếu '( ) 0 fx với xI ( hoặc '( ) 0 fx với xI ) và '( ) 0 fx tại một số hữu hạn điểm của I thì hàm số f đồng biến (hoặc nghịch biến) trên I . Vận dụng định lí trên vào các hàm số thường gặp trong chương trình. Nếu hàm số f là hàm đa thức (không kể hàm số hằng) hoặc () () Px fx Qx (trong đó Px là đa thức bậc hai , Qx là đa thức bậc nhất và Px không chia hết cho Qx thì hàm số f đồng biến (nghịch biến ) trên K , '( ) 0 ( '( ) 0) x K f x f x . Nếu hàm số f là hàm nhất biến () ax b fx cx d với , , , a b c d là các số thực và 0 ad bc thì hàm số f đồng biến (nghịch biến ) trên K , '( ) 0( '( ) 0). x K f x f x B. PHƯƠNG PHÁP GIẢI TOÁN. DẠNG 1. XÉT TÍNH ĐƠN ĐIỆU CỦA HÀM SỐ 1. Phương pháp . Bước 1. Tìm tập xác định của hàm số . f Bước 2. Tính đạo hàm () fx và tìm các điểm 0 x sao cho 0 () fx = 0 hoặc 0 () fx không xác định . Bước 3. Lập bảng xét dấu () fx , dựa vào định lí 1, nêu kết luận về các khoảng đồng biến, nghịch biến của hàm số . 2. Bài tập minh họa . Bài tập 1. Tìm các khoảng đồng biến, nghịch biến (hoặc xét chiều biến thiên) của hàm số: 1). 32 4 23 3 y x x x 2). 32 6 9 3 y x x x Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 3 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Bài tập 2. Tìm các khoảng đồng biến, nghịch biến (hoặc xét chiều biến thiên) của hàm số: 1). 42 13 1 42 y x x . 2). 43 1 41 4 y x x x Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Bài tập 3. Tìm các khoảng đồng biến, nghịch biến (hoặc xét chiều biến thiên) của hàm số: 1). 2 1 x y x 2). 21 1 x y x Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Bài tập 4. Tìm các khoảng đồng biến, nghịch biến (hoặc xét chiều biến thiên) của hàm số: 1). 2 44 1 xx y x 2). 2 4 5 5 1 xx y x Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 4 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Bài tập 5. Tìm các khoảng đồng biến, nghịch biến (hoặc xét chiều biến thiên) của hàm số: 1). 2 23 y x x 2). 2 4 3 2 3 y x x x Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Nhận xét: Bài toán xét tính đơn điệu của hàm số được chuyển về bài toán xét dấu của một biểu thức ( ' y ). Khi tính đạo hàm của hàm số có dạng () y f x ta chuyển trị tuyệt đối vào trong căn thức 2 () y f x , khi đó tại những điểm mà ( ) 0 fx thì hàm số không có đạo hàm. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 5 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Bài tập 6. Tìm các khoảng đồng biến , nghịch biến (hoặc xét chiều biến thiên) của hàm số: 1). 2 45 44 x y x 2). 2 12 1 12 2 x y x 3). 2 2 31 1 xx y xx Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Bài tập 7. Tìm các khoảng đồng biến, nghịch biến (hoặc xét chiều biến thiên) của hàm số: 1). 2 y x 2 xx 2). 2 2 1 9 y x x 3). 2 20 y x x . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 6 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Bài tập 8. Tìm các khoảng đồng biến, nghịch biến (hoặc xét chiều biến thiên) của hàm số: 1). 2sin cos 2 y x x với 0; x 2). sin 2 2cos 2 y x x x với ; 22 x Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 7 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu hỏi trắc nghiệm Mức độ 1. Nhận biết Câu 1. Cho hàm số 3 3. y x x Mệnh đề nào dưới đây đúng? A. Hàm số đồng biến trên khoảng ;1 và nghịch biến trên khoảng 1; . B. Hàm số đồng biến trên khoảng ( ; ). C. Hàm số nghịch biến trên khoảng ;1 và đồng biến trên khoảng 1; D. Hàm số nghịch biến trên khoảng 1;1 . 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Câu 2.Các khoảng đồng biến của hàm số 3 3 y x x là A. 0; . B. 0;2 . C. . D. ;1 và 2; Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 3. Tìm tất cả các khoảng đồng biến của hàm số 32 1 2 3 1 3 y x x x . A. 1;3 . B. ;1 và 3; . C. ;3 . D. 1; . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 8 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 4. Cho hàm số 32 3 5. y x x Mệnh đề nào dưới đây đúng? A. Hàm số nghịch biến trên khoảng ;0 . B . Hàm số nghịch biến trên khoảng 0;2 . C. Hàm số nghịch biến trên khoảng 2; . D. Hàm số đồng biến trên khoảng 0;2 . 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Câu 5. Cho hàm số 3 32 y x x . Mệnh đề nào dưới đây là đúng? A. Hàm số đồng biến trên khoảng ;0 và nghịch biến trên khoảng 0; . B. Hàm số nghịch biến trên khoảng ;0 và đồng biến trên khoảng 0; . C. Hàm số đồng biến trên khoảng ; . D. Hàm số nghịch biến trên khoảng ; Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 6. Hàm số 4 2 yx nghịch biến trên khoảng nào? A. 1 ; 2 . B. ;0 . C. 1 ; 2 . D. 0; . 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Câu 7. Cho hàm số 42 25 y x x . Kết luận nào sau đây đúng? A. Hàm số đồng biến trên khoảng ;1 . B. Hàm số nghịch biến với mọi x . C. Hàm số đồng biến với mọi x . D. Hàm số đồng biến trên khoảng 1;0 và 1; . Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 9 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 8. Hàm số 4 2 21 4 x yx đồng biến trên khoảng A. ;1 . B. ;0 . C. 1; . D. 0; . 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Câu 9. Hàm số 2 44 y x x đồng biến trên khoảng nào trong các khoảng sau đây? A. ;2 . B. ; . C. 2; . D. 2; . 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Câu 10. Tìm các khoảng đồng biến của hàm số 42 23 y x x . A. 1;0 và 1; . B. ;1 và 0;1 . C. 0; . D. ;0 . 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Câu 11. Cho hàm số 1 2 x y x . Khẳng định nào sau đây đúng? A. Hàm số đã cho đồng biến trên từng khoảng xác định của nó. B. Hàm số đã cho nghịch biến trên . C. Hàm số đã cho đồng biến trên khoảng ;2 2; . D. Hàm số đã cho nghịch biến trên từng khoảng xác định của nó. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 10 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 12. Kết luận nào sau đây về tính đơn điệu của hàm số 21 1 x y x là đúng? A. Hàm số nghịch biến trên . B. Hàm số đồng biến trên mỗi khoảng ;1 và 1; . C. Hàm số đồng biến trên . D. Hàm số nghịch biến trên \1 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 13. Cho hàm số 21 1 x y x . Mệnh đề nào sau đây đúng? A. Hàm số nghịch biến trên ;1 và 1; . B. Hàm số đồng biến trên \1 . C. Hàm số đồng biến trên ;1 và 1; . D. Hàm số đồng biến trên ;1 1; . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 14. Cho hàm số 1 1 x y x . Khẳng định nào sau đây đúng? A. Hàm số nghịch biến trên \1 . B. Hàm số đồng biến trên \1 . C. Hàm số đồng biến trên các khoảng ;1 và 1; . D. Hàm số đồng biến trên ; 1 1; . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 11 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 15. Cho hàm số 1 . 1 x y x Khẳng định nào sau đây là đúng? A. Hàm số đã cho nghịch biến trên khoảng ;1 . B. Hàm số đã cho đồng biến trên khoảng ;1 và khoảng 1; . C. Hàm số đã cho đồng biến trên khoảng 0; . D. Hàm số đã cho nghịch biến trên tập \1 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 16. Trong các hàm số sau, hàm số nào đồng biến trên . A. 42 1 y x x . B. 3 1 yx . C. 41 2 x y x . D. tan yx . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 17. Trong các hàm số sau, hàm số nào đồng biến trên ? A. 2 y xx . B. 42 y xx . C. 3 y xx . D. 1 3 y x x Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 18. Trong các hàm số dưới đây, hàm số nào không đồng biến trên ? A. sin 3 . y x x B. cos 2 . y x x C. 32 5 1. y x x x D. 5 . yx Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 12 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 19. Trong các hàm số sau, hàm số nào luôn nghịch biến trên ? A. sin y x x . B. 32 3 y x x . C. 23 1 x y x . D. 42 31 y x x . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 20. Trong các hàm số sau, hàm số nào đồng biến trên ? A. tan yx . B. 42 1 y x x . C. 3 1 yx . D. 41 2 x y x . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 21. Hàm số nào sau đây không đồng biến trên khoảng ; ? A. 3 1 yx . B. 1 yx . C. 2 1 x y x . D. 53 10 y x x Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 22. Hàm số nào sau đây nghịch biến trên từng khoảng xác định? A. 42 y x x . B. 32 3 y x x . C. 2 sin y x x . D. 1 2 x y x . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Mức độ 2. Thông hiểu Câu 22. Trong các hàm sau đây, hàm số nào không nghịch biến trên . A. 32 27 y x x x . B. 4 cos y x x . C. 2 1 1 y x . D. 2 23 x y Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 13 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 23. Cho hàm 2 65 y x x . Mệnh đề nào sau đây là đúng? A. Hàm số đồng biến trên khoảng 5; . B. Hàm số đồng biến trên khoảng 3; . C. Hàm số đồng biến trên khoảng ;1 . D. Hàm số nghịch biến trên khoảng ;3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 24. Hàm số 2 2 y x x nghịch biến trên khoảng nào dưới đây? A. ;1 . B. 1;2 . C. 1; . D. 0;1 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 26. Hàm số nào dưới đây đồng biến trên khoảng ; A. 3 3 y x x . B. 1 2 x y x . C. 1 3 x y x . D. 3 3 y x x . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 14 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 27. Trong các hàm số sau, hàm số nào đồng biến trên ? A. Hàm số 2 . 1 x y x B. Hàm số 3 3 5. y x x C. Hàm số 42 2 3. y x x D. Hàm số tan . yx Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 28. Trong các hàm số sau, hàm số nào không đồng biến trên tập số thực? A. 4 3sin cos . y x x x B. 32 3 2 7. y x x x C. 3 4. yx x D. 3 . y x x Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 30. Hàm số nào sau đây là hàm số đồng biến trên ? A. tan yx . B. 1 x y x . C. 2 1 x y x . D. 32 22 y x x x . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 31. Biết rằng các số thực a , b thay đổi sao cho hàm số luôn 33 3 f x x x a x b đồng biến trên khoảng ; . Tìm giá trị nhỏ nhất của biểu thức 22 4 4 2 P a b a b . A. 4 . B. 2 . C. 0 . D. 2 . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 15 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 32. Hàm số 2 82 y x x đồng biến trên khoảng nào sau đây? A. 1; . B. 1;4 . C. ;1 . D. 2;1 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 33. Cho các hàm số 1 1 x y x ; 42 22 y x x ; 32 31 y x x x . Trong các hàm số trên, có bao nhiêu hàm số đơn điệu trên ? A. 3 . B. 1. C. 2 . D. 0 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 34. Tìm tất cả các khoảng nghịch biến của hàm số: 2 22 1 xx y x . A. ;1 và 1; . B. 2;0 . C. 2; 1 và 1;0 . D. ;2 và 0; . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 16 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 35. Hàm số 2 2 y x x nghịch biến trên khoảng A. 0;1 . B. ;1 . C. 1; . D. 1;2 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 36. Có bao nhiêu hàm số đồng biến trên tập xác định của chúng trong các hàm số sau: 32 1 1 : 3 4 3 y x x x ; 21 2: 21 x y x ; 2 3 : 4 yx 3 4 : sin y x x x ; 42 5 : 2 y x x . A. 5 . B. 2 . C. 4 . D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 37. Cho hàm số y f x có đạo hàm trên và 0 fx 0; x . Biết 12 f . Khẳng định nào dưới đây có thể xảy ra? A. 21 f . B. 2017 2018 ff . C. 12 f . D. 2 3 4 ff . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 17 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 38. Cho hàm số y f x có đạo hàm 2 2 f x x x , x . Hàm số 2 y f x đồng biến trên khoảng A. 0;2 . B. 2; . C. ;2 . D. 2;0 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 39. Cho hàm số y f x thỏa mãn 2 5 4. f x x x Khẳng định nào sau đây là đúng? A. Hàm số đã cho đồng biến trên khoảng ;3 . B. Hàm số đã cho nghịch biến trên khoảng 2;3 . C. Hàm số đã cho nghịch biến trên khoảng 3; . D. Hàm số đã cho đồng biến trên khoảng 1;4 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 40. Cho hàm số y f x có đạo hàm 2 1 2 3 f x x x x . Mệnh đề nào dưới đây đúng? A. Hàm số nghịch biến trên khoảng 3;2 . B. Hàm số nghịch biến trên các khoảng 3; 1 và 2; . C. Hàm số đồng biến trên các khoảng ;3 và 2; . D. Hàm số đồng biến trên khoảng 3;2 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 41. Cho hàm số y f x có đạo hàm 2 1 1 5 f x x x x . Mệnh đề nào sau đây đúng ? A. 1 4 2 f f f . B. 1 2 4 f f f . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 18 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 C. 2 1 4 f f f . D. 4 2 1 fff . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 42. Cho hàm số fx có đạo hàm 23 1 1 2 f x x x x . Hỏi hàm số đồng biến trên khoảng nào dưới đây? A. 2; . B. 1;2 . C. ;1 . D. 1;1 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 43. Cho hàm số y f x có đồ thị như hình bên. Đặt 3 h x x f x . Hãy so sánh 1 h , 2 h , 3 h ? A. 1 2 3 h h h . B. 213 h h h . C. 3 2 1 h h h . D. 3 2 1 h h h . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 19 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 44. Cho hàm số y f x có đạo hàm 3 2 f x x x , với mọi x . Hàm số đã cho nghịch biến trên khoảng nào dưới đây? A. 1; 3 . B. 1; 0 . C. 0; 1 . D. 2; 0 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 45. Hàm số nào sau đây đồng biến trên ? A. 2 7 2 1 y x x x . B. 3 2 23 y x x . C. 2 41 y x x x . D. 3 25 yx . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu 46.(THPT chuyên Phan Bội Châu) Hàm số 2 2 y x x x nghịch biến trên khoảng. A. 1;2 . B. ;1 . C. 1; . D. 0;1 . 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 20 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 DẠNG 2. Xác định tham số m để hàm số y f x đơn điệu trên một khoảng. Loại 1. Xác định tham số để hàm số y f x đơn điệu trên . 1. Phương pháp . ① Bước 1. Xác định tham số để hàm số f xác định trên khoảng đã cho. ② Bước 2. Tính , fx vận dụng định lí 1 vào các hàm số thường gặp trong chương trình (xem phần tóm tắt giáo khoa). ③ Bước 3. Để giải bài toán dạng này ,ta thường sử dụng các tính chất sau. Nếu 2 0 f x ax bx c a thì Hàm số đồng biến trên x (hay bớt đi một số hữu hạn điểm) khi và chỉ khi 0 ( ) 0, 0 f x x a . Hàm số nghịch biến trên x (hay bớt đi một số hữu hạn điểm) khi và chi khi , . 0 ( ) 0 0 f x x a Nếu 0 ax b f x ad cb cx d thì Hàm số đồng biến trên tập xác định \ d c khi 0 . ad bc . Hàm số nghịch biến trên tập xác định \ d c khi 0 ad bc . 2. Bài tập minh họa . Bài tập 9. Có bao nhiêu giá trị nguyên của a để hàm số 32 1 43 3 y x ax x đồng biến trên Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Bài tập 10. Có bao nhiêu giá trị nguyên của tham số m để hàm số: 1). 3 22 ( 2) ( 2) (3 1) 3 x y m m x m x m đồng biến trên . 2). 32 ( 1) 3( 1) 3(2 3) y m x m x m x m nghịch biến trên và m thuộc 2020;2020 . 3). 2 3 2 1 1 1 3 3 y m x m x x luôn nghịch biến trên . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 21 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Bài tập 11. Tìm m để các hàm số sau luôn nghịch biến trên mỗi khoảng xác định . 1). 32 mx m y xm 2). 2 2 2 3 1 1 x m x m y x . Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 22 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu hỏi trắc nghiệm Mức độ 1. Nhận biết Câu 47.(Sở GD&ĐT Bình Phước 2020) Cho hàm số 32 y ax bx cx d đồng biến trên R khi A. 2 ;0 30 a b c b ac . B. 2 0 0; 3 0 abc a b ac . C. 2 0; 0 0; 3 0 a b c a b ac . D. 2 0; 0 0; 3 0 a b c a b ac . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 48.(THPT Xuân Hòa 2018) Cho hàm số 32 y ax bx cx d . Hỏi hàm số luôn đồng biến trên khi nào? A. 2 0, 0 0; 3 0 a b c a b ac . B. 2 0 0; 3 0 abc a b ac . C. 2 0, 0 0; 3 0 a b c a b ac . D. 2 0, 0 0; 3 0 a b c a b ac . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 49.(Chuyên Bắc Ninh 2018) Cho hàm số 32 1 3 2 f x x m x x .Tìm tất cả các giá trị nguyên của tham số m để 0, f x x A. 2 B. 3. C. 4. D. 5. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 23 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 50.(Trần Kỳ Phong Quãng Nam-2018) Cho hàm số 32 31 y x x mx . Có bao nhiêu giá trị nguyên âm của m để hàm số nghịch biến trên . A. 3 . B. Vô số. C. 0 . D. 1. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 51.(THPT Nguyễn Khuyến 2018) Cho hàm số 32 1 3 1 y x m x x , với m là tham số. Gọi S là tập hợp các giá trị nguyên của m để hàm số đồng biến trên khoảng ; . Tìm số phần tử của S . A. 7 . B. 6 . C. Vô số. D. 5 Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 52.(THPT Thạch Thành-Thanh Hóa 2018) Có bao nhiêu giá trị nguyên tham số m , hàm số 32 32 y x mx m x m đồng biến trên ? A. 0 . B. 1. C. 2 . D. 3 Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 53.(THPT Chuyên Lam-Thanh Hóa 2018) Tìm tập hợp S tất cả các giá trị của tham số thực m để hàm số 3 2 2 3 1 3 x y mx m x đồng biến trên . A. ; 3 1; . B. 1;3 . C. ; 1 3; . D. 1;3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 24 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 54.(THPT Cổ Loa-Hà Nội 2018) Có bao nhiêu số nguyên m để hàm số 32 6 6 6 y x mx x đồng biến trên ? A. 1. B. 2 . C. 3 . D. 0 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 55. (THPT Lê Quý Đôn 2020) Tìm m để hàm số 32 3 3 2 1 1 y x mx m đồng biến trên . A. Không có giá trị m thỏa mãn. B. 1 m . C. 1 m . D. Luôn thỏa mãn với mọi m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 56.(SGD Ninh Bình năm 2017-2018) Có tất cả bao nhiêu giá trị nguyên của tham số m để hàm số 32 11 2018 32 y x mx x đồng biến trên ? A. 5 . B. 3 . C. 4 . D. 2 . 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Câu 57.(THPT Chuyên Quốc Học-Huế 2018)Có tất cả bao nhiêu giá trị nguyên của tham số m để hàm số 32 2 3 5 3 m y x mx m x đồng biến trên . A. 6 . B. 2 . C. 5 . D. 4 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 25 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 58.(THPT Sơn Tây-Hà Nội-2018) Tìm tất cả các giá trị m để hàm số 32 2 1 2 3 m y x mx m x nghịch biến trên tập xác định của nó. A. 0 m . B. 1 m . C. 2 m . D. 0 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 59.(THPT Lương Văn Chánh 2018) Cho hàm số: 32 1 1 2 5 y m x m x x với m là tham số. Có bao nhiêu giá trị nguyên của m để hàm số nghịch biến trên khoảng ; . A. 5 . B. 6 . C. 8 . D. 7 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 60.(THPT Chuyên Hoàng Văn Thụ-2018) Số các giá trị nguyên của tham số m trong đoạn 100;100 để hàm số 32 13 y mx mx m x nghịch biến trên là: A. 200 . B. 99 . C. 100 . D. 201. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 26 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 61.(THPT Hoàng Hoa Thám-2018) Số giá trị nguyên của m để hàm số 2 3 2 (4 ) ( 2) 1 y m x m x x m 1 đồng biến trên bằng. A. 5 . B. 3 . C. 2 . D. 4 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 62.(THPT Chuyên Hùng Vương 2018) Có bao nhiêu giá trị nguyên của tham số m trong khoảng 2019;2019 để hàm số 2 3 2 4 3 2 3 4 f x m x m x x đồng biến trên . A. 2016 . B. 2017 . C. 2019 . D. 2018 Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 63.(THPT Chuyên Lương Văn Tụy 2018) Có bao nhiêu giá trị nguyên của tham số m trong khoảng 2019;2019 để hàm số 32 1 3 1 3 2 5 y m x m x m x m nghịch biến trên là A. 2019 . B. 2020 . C. 2022 . D. 2021. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 27 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 64.(THPT Chuyên Hùng Vương 2018) Hỏi có bao nhiêu giá trị nguyên m để hàm số 2 3 2 1 1 4 y m x m x x nghịch biến trên khoảng ; ? A. 1. B. 2 . C. 0 . D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 65.(THPT Lục Ngạn 2018) Cho hàm số 32 4 9 5 y x mx m x , với m là tham số. Có bao nhiêu giá trị nguyên của m để hàm số nghịch biến trên ; ? A. 5 . B. 6 . C. 7 . D. 4 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 66.(Lương Văn Chánh Phú yên-2018) Cho hàm số: 32 1 1 2 5 y m x m x x với m là tham số. Có bao nhiêu giá trị nguyên của m để hàm số nghịch biến trên khoảng ; ? A. 5 . B. 6 . C. 8 . D. 7 . 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 28 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 67.(Chuyên Quốc Học Huế 2018) Có tất cả bao nhiêu giá trị nguyên của tham số m để hàm số 2 3 3 1 mm yx x đồng biến trên từng khoảng xác định của nó? A. 4 . B. 2 . C. 1. D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 68.(Sở GD&ĐT Bắc Giang 2018) Có bao nhiêu giá trị nguyên của tham số m để hàm số 2 4 xm y x đồng biến trên từng khoảng xác định của nó? A. 5 B. 3 C. 1 D. 2 Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 69.(Chuyên Thái Bình-2018) Có tất cả bao nhiêu giá trị nguyên của m để hàm 4 xm y mx đồng biến trên từng khoảng xác định? A. 2 . B. 4 . C. 3 . D. 5 . 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 29 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 70.(SGD Bắc Giang-2018) Có bao nhiêu giá trị nguyên của tham số m để hàm số 2 4 xm y x đồng biến trên từng khoảng xác định của nó? A. 5 . B. 3 . C. 1. D. 2 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 71.(THPT Chuyên Thái Bình 2018) Có tất cả bao nhiêu giá trị nguyên của m để hàm số 4 xm y mx đồng biến trên từng khoảng xác định? A. 2 . B. 4 . C. 3 . D. 5 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 72.(THPT Kinh Môn 2018) Kết quả của m để hàm số sau 2 xm y x đồng biến trên từng khoảng xác định là A. 2 m . B. 2 m . C. 2 m . D. 2 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 73.(THPT Việt Trì-Phú Thọ-2018) Có bao nhiêu giá trị nguyên của tham số m trong khoảng 2019;2019 để hàm số 1 xm y x đồng biến trên từng khoảng xác định của chúng. A. 2017 . B. 2020 . C. 2019 . D. 2018 . Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 30 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 74.(THPT Kiến An-Hải Phòng 2018)Tìm tất cả các giá trị thực của tham số m để hàm số 2 1 xm y x đồng biến trên khoảng xác định của nó. A. 1;2 m . B. 2; m . C. 2; m . D. ;2 m Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 75.(THPT Đồng Đậu-Vĩnh Phúc 2018) Có bao nhiêu giá trị nguyên của tham số m để hàm số 2 4 1 mx y x đồng biến trên tứng khoảng xác định. A. 0 . B. 1. C. 2 . D. 3 . 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Câu 76.(THPT Kinh Môn 2 -2018) Kết quả của m để hàm số sau 2 xm y x đồng biến trên từng khoảng xác định là A. 2 m . B. 2 m . C. 2 m . D. 2 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 77.(THPT Chuyên Thái Bình 2018) Tìm tất cả các giá trị thực của tham số m để hàm số sin y mx x đồng biến trên . A. 1 m . B. 1 m . C. 1 m . D. 1 m . 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 31 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Loại 2. Xác định tham số để hàm số y f x đơn điệu trên khoảng ; ab , nữa khoảng ; a … 1. Phương pháp. ⋇ Cách 1. Biện luận ( đối với cách này phương trình 0 y có 2 cx d ) Bước 1. Tập xác định và tính đạo hàm y . Bước 2. Giải phương trình 1 2 0. theom h x om y x te (công thức 1 2 b x a , 2 2 b x a ) Bước 3. Lập bảng biến thiên biện luận. ⋇ Cách 2. Áp dụng công thức dấu của tam thức bậc hai. Bước 1. Tập xác định và tính đạo hàm y . Bước 2. Nếu y là một tam thức bậc hai có dạng 2 . ,0 y Ax BX C A Khi đó, ① Nếu 0 0, 0 yx a suy ra hàm số đồng biến trên khoảng ; ab , ; a … ② Nếu 0 0, 0 yx a suy ra hàm số nghịch biến trên khoảng ; ab , ; a … ③ 0 thì 0 y có hai nghiệm 12 , xx , khi đó 12 . 0 .0 2 x x Ay S ④ 0 thì 0 y có hai nghiệm 12 , xx , khi đó 12 0 . . 0 2 x x Ay S ⑤ 0 thì 0 y có hai nghiệm 12 , xx , khi đó 12 . .0 .0 Ay xx Ay ⋇ Cách 3. Cô lập tham số m , tức là biến đổi , 0 0 . f x m g x m m Bước 1. Xác định tham số để hàm số f xác định trên khoảng đã cho. Bước 2. Tính , f x m , vận dụng định lí 1 vào các hàm số thường gặp trong chương trình. Bước 3. Để giải bài toán dạng này, ta thường sử dụng các tính chất sau. Nếu hàm số đồng biến trên ; ab thì ( ) 0, ; f x x a b Coâlaäpthams m oá ; , ; min . ab g x h m x a b g x h m Nếu hàm số nghịch biến trên ; ab thì ( ) 0, ; f x x a b Coâlaäpthams m oá ; , ; max . ab g x h m x a b g x h m Nếu 0 ax b f x ad cb cx d có tập xác định \ d D c thì Hàm số đồng biến trên ; L khi 2 0, ; ac bd xL cx d Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 32 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 0 ; ac bd d L c 0 . ac bd d L c Hàm số nghich biến trên ; L khi 2 0, ; ac bd xL cx d 0 ; ac bd d L c 0 . ac bd d L c Lưu ý: trong một số bài toán tham số m có chứa tham số m bậc hai và bậc một thì không thể cô lập m được nên ta phải biện luận. Gọi S tập nghiệm của .0 A f x thì S hoặc 12 ; ; . S x x Khi đó điều kiện: . 0, ; ; . A f x x a b a b S Khi đó điều kiện: 12 . 0, ; ; ; . A f x x a b a b x x 2. Bài tập minh họa . Bài tập 12. Tìm các giá trị của tham số m để hàm số : 1). 21 x y xm nghịch biến trên (2; ) 2). 32 ( 2) (3 2) 2 y x m x m x đồng biến trên đoạn 3;4 Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 33 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Bài tập 13. Tập hợp tất cả giá trị của tham số m để hàm số 1 4 mx y mx nghịch biến trên khoảng 1 ; 4 là ? Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Bài tập 14. Có tất cả bao nhiêu giá trị nguyên của tham số m để hàm số 10 2 mx y xm nghịch biến trên khoảng 0;2 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Bài tập 15. Hàm số 2 ( 1) 2 6 1 m x mx m y x . Tìm các giá trị của tham số m để hàm số: 1). Đồng biến trên mỗi khoảng xác định của nó; 2). Đồng biến trên khoảng 4; Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 34 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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.................................................................................................................................................................................................................... .................................................................................................................................................................................................................... ◆ Bài toán: Cho hàm số y x f u xác định và có đạo hàm trên ; ... ab Xác định tham số m để hàm số f đồng biến (nghịch biến) trên ; ... ab . ◆ Nhận xét: đối với các bài toán đặc ẩn phụ ta sử dụng tính chất sau: ⋇ Tính chất: đặt ;; ; min ma , x a b a b t x a b t t u x t khi đó y f f ux t ① Nếu y x f u đồng biến trên ; ... ab và t u x đồng biến trên ; ... ab thì y f t cũng đồng biến trên ;; . min x ;ma a b a b tt ② Nếu y x f u đồng biến trên ; ... ab và t u x nghịch biến trên ; ab thì y f t nghịch biến trên ;; . min x ;ma a b a b tt ③ Nếu y x f u nghịch biến trên ; ... ab và t u x đồng biến trên ; ab thì y f t nghịch biến trên ;; . min x ;ma a b a b tt ④ Nếu y x f u nghịch biến trên ; ab và t u x nghịch biến trên ; ab thì y f t đồng biến trên ;; . min x ;ma a b a b tt 3. Bài tập minh họa Bài tập 16. Tìm các giá trị của m để hàm số 2sin 1 sin x y xm đồng biến trên khoảng 0; 2 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 35 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Bài tập 17. Tìm các giá trị m để hàm số cot 2 cot x y xm nghịch biến trên ; 42 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 3. Câu hỏi trắc nghiệm Mức độ 1. Nhận biết Câu 78.(THPT Lê Hoàn Thanh Hóa 2018) Tìm tất cả các giá trị thực của m để hàm số 32 3 1 3 2 1 y x m x m m x đồng biến trên các khoảng thỏa mãn 12 x . A. 12 2 3 m m m . B. 10 m . C. 4 2 m m . D. 2 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 36 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 79.(Sở GD-ĐT Quãng Nam 2018) Có bao nhiêu giá trị nguyên của tham số m để hàm số 3 2 2 3 2 3 4 1 y x m x m m x nghịch biến trên khoảng 0;1 . A. 1. B. 4 . C. 3 . D. 2 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 80.(THPT Trần Phú - Đà Nẵng-2018) Có bao nhiêu giá trị nguyên âm của tham số m để hàm số 32 1 1 2 3 1 3 y x m x m x đồng biến trên khoảng 1; . A. 3 . B. 1. C. 0 . D. Vô số. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 81.(THPT NEWTON Hà Nội 2018) Có bao nhiêu số nguyên dương m để hàm số 3 2 2 2 (2 9) 2( 9 ) 10 3 y x m x m m x nghịch biến trên khoảng 3;6 ? A. 4 . B. 6 . C. 7 . D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 37 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 82.(Chuyên Hùng Vương Phú Thọ) Tìm tập hợp S tất cả các giá trị của tham số thực m để hàm số 3 2 2 1 1 2 3 3 y x m x m m x nghịch biến trên khoảng 1;1 . A. 1;0 S B. S . C. 1 S . D. 0;1 S Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 83.(THTT Số 3-486-2018) Tìm tất cả các giá trị thực của tham số m để hàm số 3 2 2 39 y x mx m x nghịch biến trên khoảng 0;1 . A. 1 3 m . B. 1 m . C. 1 3 m hoặc 1 m . D. 1 1 3 m . 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Câu 84.(THPT Thạch Thành 2018) Tìm tập hợp S tất cả các giá trị của tham số thực m để hàm số 3 2 2 1 1 2 3 3 y x m x m m x nghịch biến trên khoảng 1;1 . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 38 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 A. 1;0 S . B. 1 S . C. 0;1 S . D. S . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 85.(Sở GD&ĐT Bắc Giang 2018) Có bao nhiêu giá trị nguyên không âm của tham số m để hàm số 42 2 3 1 y x mx m đồng biến trên khoảng 1;2 . A. 1 B. 4 C. 2 D. 3 Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 86.(Chuyên Đại Học Vinh 2018) Số giá trị nguyên của 10 m để hàm số 2 ln 1 y x mx đồng biến trên 0; là A. 10 . B. 11. C. 8 . D. 9 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 39 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 87.(THPT Quãng Xương-2018) Có bao nhiêu giá trị nguyên của tham số m để hàm số 1 4 mx y mx nghịch biến trên khoảng 1 ; 4 . A. 0 . B. 1. C. 2 . D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 88.(THPT Hậu Lộc 2-Thanh Hóa 2018) Có bao nhiêu giá trị nguyên của tham số m để hàm số 1 2 2 m x m y xm nghịch biến trên khoảng 1; . A. 0 . B. 1. C. 2 . D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 89.(THPT Chuyên Trần Phú 2018) Tìm tất cả các giá trị thực của tham số m để trên 1;1 hàm số 6 21 mx y xm nghịch biến: A. 43 m . B. 43 13 m m . C.14 m . D. 43 13 m m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 40 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 90.(THPT Mộ Đức-2018) Tồn tại bao nhiêu số nguyên m để hàm số 2 x y xm đồng biến trên khoảng ;1 . A. 3 . B. 4 . C. 2 . D. Vô số. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 91.(Sở GD-ĐT Gia Lai-2018) Tìm tất cả giá trị thực của tham số m để hàm số 4 mx y mx nghịch biến trên khoảng 3;1 . A. 1;2 m . B. 1;2 m . C. 1;2 m . D. 1;2 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 92.(THPT Lê Qúy Đôn 2018) Tìm tất cả các giá trị thực của tham số m sao cho hàm số 4 mx y xm nghịch biến trên khoảng ;1 ? A. 21 m . B. 21 m . C. 22 m . D. 22 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 41 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 93.(THPT Đức Thọ-2018) Cho hàm số 2015 2016 mx m y xm với m là tham số thực. Gọi S là tập hợp các giá trị nguyên của m để hàm số đồng biến trên từng khoảng xác định. Tính số phần tử của S . A. 2017 . B. 2015 . C. 2018 . D. 2016 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 94.(THPT Kim Liên-2018) Cho hàm số 2 2 mx y xm , m là tham số thực. Gọi S là tập hợp tất cả các giá trị nguyên của tham số m để hàm số nghịch biến trên khoảng 0;1 . Tìm số phần tử của S . A. 1. B. 5 . C. 2 . D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 95.(Đề Chính Thức Bộ giáo Dục 2018) Có bao nhiêu giá trị nguyên của tham số m để hàm số 1 3 x y xm nghịch biến trên khoảng 6; ? A. 3 . B. Vô số. C. 0 . D. 6 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 42 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 96.(Chuyên Hạ Long 2018) Tìm tất cả các giá trị thực của tham số m sao cho hàm số tan 2 tan x y xm đồng biến trên khoảng ;0 . 4 A. 12 m . B. 2 m . C. 2 m . D. 1 02 m m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu 97.(THPT Kinh Môn năm 2020) Tìm tất cả các số thực của tham số m sao cho hàm số 2sin 1 sin x y xm đồng biến trên khoảng 0; 2 . A. 1 0 2 m hoặc 1 m . B. 1 2 m . C. 1 2 m . D. 1 0 2 m hoặc 1 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 43 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu 98.(THPT Phan Đình Phùng 2018) Tất cả các giá trị của m để hàm số 2cos 1 cos x y xm đồng biến trên khoảng 0; 2 là: A. 1 m . B. 1 2 m . C. 1 2 m . D. 1 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu 99.(THPT Chuyên Nguyễn Quang Diệu –2018) Cho hàm số ln 6 ln 2 x y xm với m là tham số. Gọi S là tập hợp các giá trị nguyên dương của m để hàm số đồng biến trên khoảng 1;e . Tìm số phần tử của S . A. 1. B. 2 . C. 4 . D. 3 Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 44 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 100.(Chuyên Đại Học Sư phạm-2018) Giá trị m để hàm số cot 2 cot x y xm nghịch biến trên ; 42 là A. 0 m . B. 0 12 m m . C. 12 m . D. 2 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 101.(THPT Chuyên Vĩnh Phúc-2018) Tìm tất cả các giá trị thực của tham số m để hàm số sin 3 sin x y xm đồng biến trên khoảng 0; 4 . A. 0 m hoặc 2 3. 2 m B. 3. m C. 0 m hoặc 2 3. 2 m D. 0 3. m Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 45 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 102.(THPT Nguyễn Đức Thuận 2018) Tìm tất cả các giá trị thực của tham số m để hàm số 2 cos sin mx y x đồng biến trên khoảng ; 32 . A. 0 m . B. 2 m . C. 1 m . D. 5 4 m . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu 103.(SGD Bắc Giang-2018) Có bao nhiêu giá trị nguyên không âm của tham số m để hàm số 42 2 3 1 y x mx m đồng biến trên khoảng 1;2 . A. 1. B. 4 . C. 2 . D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 104.(THPT Chuyên Hạ Long 2018) Gọi S là tập hợp các giá trị nguyên dương của m để hàm số 32 3 2 1 12 5 2 y x m x m x đồng biến trên khoảng 2; . Số phần tử của S bằng A. 1. B. 2 . C. 3 . D. 0 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 46 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu 105.(Chuyên Vĩnh Phúc Lần 4-2018) Có bao nhiêu giá trị nguyên dương của tham số m để hàm số 42 4 31 1 44 y x m x x đồng biến trên khoảng 0; . A. 1. B. 2. C. 3. D. 4. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu 106.(Chuyên KHTN-2018) Tập hợp tất cả các giá trị của tham số m để hàm số 32 61 y x mx m x đồng biến trên khoảng 0;4 là: A. ;6 . B. ;3 . C. ;3 . D. 3;6 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 47 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 107.(THPT Yên Lạc Vĩnh Phúc 2018) Tìm tất cả các giá trị của tham số m để hàm số 32 31 y x x mx đồng biến trên khoảng ;0 . A. 2 m . B. 3 m . C. 1 m . D. 0 m . 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Câu 108.(THPT Hồng Bàng 2018) Cho hàm số 3 2 2 2 3 1 3 x y m x m x . Giá trị nguyên lớn nhất của m để hàm số đã cho nghịch biến trên đoạn 0;3 là A. 2 . B. 2 . C. 1 . D. 1. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 48 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 109.(THPT Chuyên ĐH Vinh 2018) Có bao nhiêu giá trị nguyên của tham số m trong khoảng 2019;2019 để hàm số 32 12 1 2 3 33 y x m x m x đồng biến trên 1; A. 2019 . B. 2018 . C. 2020 . D. 2016 . Lời giải. .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 110.(THPT Yên Lạc-2018) Cho hàm số: 3 2 1 3 4 3 x y a x a x . Tìm a để hàm số đồng biến trên khoảng 0; 3 A. 12 7 a . B. 3 a . C. 3 a . D. 12 7 a . 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 49 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 101.(THPT Việt Trì-Phú Thọ 2018) Có bao nhiêu giá trị nguyên của m để hàm số 3 2 2 3 3 2 5 y x x m m x đồng biến trên 0; 2 ? A. 3 . B. 2 . C. 4 . D. 1. Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Câu 102.(THPT Chuyên ĐH Vinh 2018) Có bao nhiêu giá trị nguyên 10;10 m để hàm số 2 4 2 2 4 1 1 y m x m x đồng biến trên khoảng 1; ? A. 15. B. 6 . C. 7 . D. 16 . 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Câu 103.(Chuyên Đại Học Vinh 2018) Có bao nhiêu giá trị nguyên 10;10 m để hàm số 2 4 2 2 4 1 1 y m x m x đồng biến trên khoảng 1; ? A. 15. B. 6 . C. 7 . D. 16 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 50 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 104.(Chuyên Phan BỘI Châu-2018) Có bao nhiêu giá trị nguyên của m để hàm số 3 sin cos y x m x x m đồng biến trên A. 5 . B. 4 . C. 3 . D. Vô số. 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Câu 105.(THPT Nguyễn Khuyến-2018) Có bao nhiêu giá trị nguyên của tham số m trong khoảng 2019;2019 hàm số 22 1 1 sin y m m x m m x luôn đồng biến trên 0;2 . A. 2019 . B. 2018 . C. 2020 . D. 2016 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 106.(THPT Hồng Lĩnh Hà Tỉnh-2018) Cho hàm số 2 1 3 2 cos y m x m x . Gọi X là tập hợp tất cả các giá trị nguyên của tham số thực m sao cho hàm số đã cho nghịch biến trên . Tổng giá trị hai phần tử nhỏ nhất và lớn nhất của X bằng A. 4 . B. 5 . C. 3 . D. 0 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 51 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 107.(THPT Bình Xuyên-2018) Tìm m để hàm số 32 3 sin sin sin 2 y m x x x m đồng biến trên khoảng ;0 2 ? A. 3 m . B. 0 m . C. 1 3 m . D. 1 3 m . 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Loại 3. Xác định tham số m để hàm số y f x đơn điệu trên khoảng có độ dài bằng L . 1. Phương pháp . Xét hàm số bậc 3: 32 0. y ax bx cx d a Bước 1. Xác định tham số để hàm số f xác định trên khoảng đã cho. Bước 2. Tính 2 , 3 2 f x m ax bx c . Bước 3. Để giải bài toán dạng này, ta thường sử dụng các tính chất sau. Nếu 2 30 b ac thì hàm số đồng biến(nghịch biến) trên nên không thỏa mãn đề bài. Nếu hàm số đồng biến thì 22 22 12 0 9 3 0 3 34 . y a aL b ac L b ac a x x L Nếu hàm số nghịch biến thì 22 22 12 0 9 3 0 3 34 . y a aL b ac L b ac a x x L 2. Bài tập minh họa . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 52 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Bài tập 14. 1). Tìm m để hàm số 3 2 (1 2 ) 1 3 x y mx m x đồng biến trên 1; . 2). Tìm m để hàm số 32 3 ( 1) 2 3 y x x m x m đồng biến trên một khoảng có độ dài nhỏ hơn 1. 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Câu hỏi trắc nghiệm Mức độ 1. Nhận biết Câu 108.(SGD Bà Rịa Vũng Tàu 2018) Gọi S là tập hợp các giá trị của tham số m để hàm số 32 11 2 3 4 32 y x mx mx m nghịch biến trên một đoạn có độ dài bằng 3 . Tính tổng tất cả phần tử của S. A. 9 . B. 1 . C. 8 . D. 8 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 53 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 109.(SGD Bà Rịa Vũng Tàu 2018) Gọi S là tập hợp các giá trị của tham số m để hàm số 32 1 1 4 7 3 y x m x x nghịch biến trên một đoạn có độ dài bằng 2 5. Tính tổng tất cả phần tử của S . A. 4 . B. 2 . C. 1 . D. 2 . 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Câu 110.(THPT Chuyên Hùng Vương 2020) Có bao nhiêu giá trị nguyên âm của tham số thực m để hàm số 32 3 1 2 3 y x x m x m đồng biến trên đoạn có độ dài lớn hơn 1? A. 0 . B. 3 . C. 1. D. 2 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 54 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... Câu 111.(THPT Ngô-Quyền Hải Phòng 2020) Biết hàm số 32 1 3 1 9 1 3 y x m x x nghịch biến trên khoảng 12 ; xx và đồng biến trên các khoảng còn lại của tập xác định. Nếu 12 63 xx thì có bao nhiêu giá trị nguyên âm của tham số m thỏa mãn đề bài? A. 0 . B. 1. C. 2 . D. 3 . Lời giải .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... .................................................................................................................................................................................................................... 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 55 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 DẠNG 3. Xác định tham số m để phương trình, bất phương trình, hệ phương trình, hệ bất phương trình có nghiệm. (Cô lập tham số m ) 1. Kiến thức bỗ trợ: Để làm dạng toán này ta nắm các kiến thức sau. Tính chất 1: Số nghiệm của phương trình ( ) ( ) f x g m chính là số giao điểm của đồ thị () y f x và đường thẳng song song với trục Ox : () y g m . Tính chất 2: Bất phương trình () f x k có nghiệm trên D khi và chỉ khi max ( ) D f x k (Nếu tồn tại max ( ) D fx ). Bất phương trình () f x k có nghiệm trên D khi và chỉ khi min ( ) D f x k (Nếu tồn tại min ( ) D fx ). Bất phương trình () f x k nghiệm đúng với mọi x thuộc D khi và chỉ khi min ( ) D f x k (Nếu tồn tại min ( ) D fx ). Bất phương trình () f x k nghiệm đúng với mọi x thuộc D khi và chỉ khi max ( ) D f x k (Nếu tồn tại max ( ) D fx ). Loại 1. Tìm m để phương trình ( , ) 0 F x m có nghiệm trên D. 2. Phương pháp. ① Bước 1. Biến đổi phương trình về dạng ( ) ( ) f x g m . ② Bước 2. Khi đó phương trình đã cho có nghiệm khi và chỉ khi đường thẳng () y g m cắt đồ thị hàm số () y f x . ③ Bước 3. Đạo hàm fx và tìm giá trị lớn nhất và nhỏ nhất trên miền D . Khi đó nếu hàm số () y f x liên tục trên ; ab thì phương trình ( ) ( ) f x g m có nghiệm trên ; ab khi và chỉ khi: [ ; ] [ ; ] min ( ) ( ) max ( ) ab ab f x g m f x . 3. Bài tập minh họa. Bài tập 18. Tìm các giá trị của tham số m để phương trình : 2 2 1 2 2 x m x x có nghiệm. 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Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 56 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Bài tập 19. Tìm các giá trị của tham số m để phương trình : 1). 2 3 6 2 6 36 x x x x m có nghiệm. 2). 2 31 21 21 x x mx x có nghiệm. 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Bài tập 20. Tìm m để các phương trình sau có nghiệm 2 2 4 2 2 4 4 16 4 4 x x x m x x m Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 57 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. 3. Câu hỏi trắc nghiệm Mức độ 1. Nhận biết Câu 112.(THPT Chuyên Vĩnh Phúc-2018) Phương trình 2 32 11 x x x m x có nghiệm thực khi và chỉ khi A. 3 6 4 m . B. 14 1 25 m . C. 4 3 m . D. 13 44 m . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 113.(THPT Thanh Miện 2018) Tìm m để bất phương trình 2 2 2 2 4 2 2 2 x x x m x x có nghiệm? A. 8 m . B. 1 4 3 m . C. 7 m . D. 87 m . Lời giải. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 58 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 114.(THPT Chuyên Lam Sơn-2018) Có bao nhiêu giá trị nguyên của tham số m để phương trình: 1 2cos 1 2sin 2 m xx có nghiệm thực. A. 3 . B. 5 . C. 4 . D. 2 Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 59 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 115.(PTNK-ĐHQG TP HCM 2018) Tìm m để phương trình 1 1 sin sin 2 x x m có nghiệm. A. 16 22 m . B. 01 m . C. 03 m . D. 6 3 2 m . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 116.(Sở GD & ĐT Hậu Giang 2018) Có bao nhiêu giá trị nguyên của tham số m để phương trình 3 3 3 3cos cos m m x x có nghiệm thực? A. 2 . B. 7 . C. 5 . D. 3 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 60 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Loại 2. Tìm m để phương trình ( , ) 0 F x m có k nghiệm trên D . (một nghiệm, hai nghiệm…) 1. Phương pháp . ① Bước 1. Biến đổi phương trình về dạng: ( ) ( ) f x g m . ② Bước 2. Khi đó phương trình đã cho có k nghiệm khi và chỉ khi đường thẳng () y g m cắt đồ thị hàm số () y f x tại k điểm có hoành độ thuộc D . ③ Bước 3. Đạo hàm fx và lập bảng biến thiên. Từ bảng biến thiên suy ra số giao điểm. 2. Bài tập minh họa . Bài tập 21. Tìm các giá trị của tham số m để phương trình sau 2 3 2 2 ( 2 ) 3( 2 ) 0 x x x x m 1). Có nghiệm. 2). Có đúng hai nghiệm thực phân biệt. Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 61 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 22. Chứng minh rằng với mọi giá trị dương của tham số m thì phương trình thì phương trình 2 2 8 ( 2) x x m x có hai nghiệm thực phân biệt. Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 23. Tìm tất cả các giá trị của m để phương trình: 2 1 cos mx x có đúng một nghiệm 0; 2 x Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 24. Tìm các giá trị của tham số m để phương trình : 2 3 3 m 0 x x x 1). Có đúng 4 nghiệm thực. 2). Có đúng một nghiệm thực dương. Lời giải. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 62 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 25. Tìm các giá trị của tham số m để phương trình 2 1 4 1 2 3 2 x x mx x có đúng hai nghiệm Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. 4. Câu hỏi trắc nghiệm Mức độ 1. Nhận biết Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 63 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 117.(THPT Chuyên Huỳnh Mẫn Đạt) Cho hàm số 42 24 y x x . Tìm m để phương trình 22 23 x x m có 2 nghiệm phân biệt ? A. 3 2 m m . B. 3 m . C. 3 2 m m . D. 2 m . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 118.(THPT Số 1 Tư Nghĩa 2019) Cho hàm số y f x liên tục trên và có đồ thị như hình vẽ dưới đây. Tập hợp tất cả các giá trị thực của tham số m để phương trình 3 2 2 3 2 3 f x x m m có nghiệm thuộc nửa khoảng 1; 3 A. 1;1 2;4 . B. 1; 2 4; . C. ; 1 2;4 . D. 1;1 2;4 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 64 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Loại 3. Tìm m để bất phương trình ( , ) 0 F x m có nghiệm trên D. 1. Phương pháp. Bước 1. Biến đổi phương trình về dạng: ( ) ( ) f x g m ( hoặc ( ) ( ) f x g m ). Bước 2. Khi đó bất phương trình ( ) ( ) f x g m có nghiệm khi và chỉ khi ( ) max ( ) D g m f x ( ) ( ) f x g m có nghiệm khi và chỉ khi ( ) min ( ) D g m f x (với điều kiện tồn tại max ( ) ( min ( )) D D f x f x . Bước 3. Đạo hàm fx và tìm giá trị lớn nhất và nhỏ nhất trên miền D . Chú ý: Khi đặt ẩn phụ ta phải tìm miền xác định của ẩn phụ và giải quyết bài toán ẩn phụ trên miền xác định vừa tìm. Cụ thể: Khi đặt ( ), t u x x D , ta tìm được tY và phương trình ( , ) 0 f x m (1) trở thành ( , ) 0 g t m (2). Khi đó (1) có nghiệm xD (2) có nghiệm tY . 2. Bài tập minh họa . Bài tập 26. Tìm các giá trị của tham số m để bất phương trình : 2 1 (2 1) 2 5 x m x x có nghiệm. Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 27. Tìm các giá trị của tham số m để bất phương trình : 2 29 m x x m có nghiệm. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 65 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 28. Tìm các giá trị của tham số m để bất phương trình 3 2 2 6 9 5 0 x x x m m nghiệm đúng với mọi 1 x . Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 29. Tìm các giá trị của tham số m để bất phương trình 2 1 2 3 2 5 3 x x m x x nghiệm đúng 1 ;3 2 x . Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 66 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Bài tập 30. Tìm các giá trị của tham số m để bất phương trình 22 3 2 3 4 x x m x x nghiệm đúng với mọi 3 x . Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 31. Tìm m để bất pt 2 2 2 1 (2 ) 0 m x x x x có nghiệm 0;1 3 x . Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 67 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Bài tập 32. Tìm m để bất phương trình : 2 (4 )(6 ) 2 x x x x m nghiệm đúng 4;6 x . Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. 5. Câu hỏi trắc nghiệm Mức độ 1. Nhận biết Câu 119.(THPT Chuyên ĐHSP-2018) Tập nghiệm của bất phương trình 2 2 2 2 3 1 3 1 0 x x x x là A. 1; . B. 1;2 . C. 1; . D. 1;2 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 120.(Sở GD-ĐT Nam Định 2018) Biết rằng bất phương trình 2 2 4 2 2 1 1 2 1 2 m x x x x x x có nghiệm khi và chỉ khi ;2 m a b , với a , b . Tính giá trị của T a b . A. 3 T . B. 2 T . C. 0 T . D. 1 T . Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 68 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. DẠNG 4. Chứng minh đẳng thức. 1. Phương pháp . Cách 1 . Bước 1. Biến đổi BĐT đã cho về dạng 0 fx ( hoặc 0 ,..) với xD . Bước 2. Lập bảng biến thiên của fx với xD . Từ đó suy ra điều phải chứng minh . Cách 2: Bước 1. Biến đổi BĐT đã cho về dạng f a f b . Nếu ab thì chứng minh fx là hàm số đồng biến trên ; ba . Nếu ab thì chứng minh fx là hàm số nghịch biến trên ; ba . Chú ý: Khi chứng minh bất đẳng thức có dạng ( ) , ; f x k x a b Nếu () k f a ta chứng minh hàm f đồng biến trên ; ab Nếu () k f b ta chứng minh hàm f nghịch biến trên ; ab . 2. Bài tập minh họa. Bài tập 33. Chứng minh rằng : sin 0; 2 x x x . Lời giải. .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 69 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. Bài tập 34. Chứng minh rằng : 3 32 xx , 2;2 x . Lời giải. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. DẠNG 5. Cho đồ thị hàm số fx hoặc bảng biến thiên fx , hoặc công thức fx tìm sự đồng biến, nghịch biến của hàm . g u x 1. Phương pháp. XÁC ĐỊNH CỰC TRỊ CỦA HÀM SỐ DỰA VÀO ĐỒ THỊ HÀM SỐ fx Đồ thị hàm số đang đi lên (đồng biến) sau đó đổi hướng đi xuống (nghịch biến) tại điểm o x thì hàm số đạt cực đại tại o x . Khi đó o fx được gọi là giá trị cực đại của hàm số fx . Đồ thị hàm số đang đi xuống sau đó đổi hướng đi lên tại điểm o x thì hàm số đạt cực tiểu tại o x Khi đó o fx được gọi là giá trị cực tiểu của hàm số fx . Hoành độ cực trị 0 xa y xb XÁC ĐỊNH CỰC TRỊ CỦA HÀM SỐ DỰA VÀO ĐỒ THỊ HÀM SỐ fx Hàm số y f x có đạo hàm fx trên D nếu: ① Đồ thị hàm số fx nằm phía trên Ox nên 0 fx . ② Đồ thị hàm số fx nằm phía dưới Ox nên 0. fx 0 xa y x b xc tức là ba nghiệm ,, abc là giao của đồ thị với trục Ox Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 70 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Bài toán: Xác định cực trị của hàm hợp y x f u dựa vào bảng biến thiên của đồ thị hàm số y f x Tương tự phương pháp xác định tính đơn điệu của hàm hợp y x f u . Xét hàm số g x f u x Bước 1: 0 .0 0 ux g x f u x u x f u x f u x . Tìm 12 ; ;....... i x x x là nghiệm của 0 fx . Bước 2: Giải phương trình 1 2 0 .......... u x x f u x u x x . Xét dấu f u x dựa vào dấu của fx hoặc dựa vào bảng biến thiên dấu fx . Vai trò của ux giống như của x vì dấu của f u x cũng là dấu của fx . Bước 3: Lập bảng xét dấu gx . 2. Bài tập minh họa. Mức độ 3. Vận dụng Câu 121. Cho hàm số fx có đạo hàm 23 1 1 2 f x x x x . Hàm số fx đồng biến trên khoảng nào dưới đây? A. 1;1 . B. 1;2 . C. ;1 . D. 2; Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 122. Cho hàm số y f x liên tục trên và có đạo hàm 2 2017 1 2 3 f x x x x .Khẳng định nào dưới đây đúng? A. Hàm số đồng biến trên các khoảng 1;2 và 3; . B. Hàm số có ba điểm cực trị. C. Hàm số nghịch biến trên khoảng 1;3 . D. Hàm số đạt cực đại tại 2 x và đạt cực tiểu tại 1 x và 3 x . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 71 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 123. Cho hàm số y f x liên tục trên và có đạo hàm 23 1 1 2 f x x x x . Hàm số y f x đồng biến trên khoảng nào dưới đây? A. 1;2 . B. ;1 . C. 1;1 . D. 2; . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 124. Cho hàm số fx có đạo hàm ' fx xác định, liên tục trên và có đồ thị ' fx như hình vẽ dưới. Hàm số fx đồng biến trên khoảng nào dưới đây? A. 2; . B. ;1 . C. 3; D. 1;3 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 125. Cho hàm số fx có đạo hàm ' fx xác định, liên tục trên và có đồ thị ' fx như hình vẽ. Khẳn g định nào sau đây là sai? A. Hàm số fx đồng biến trên khoảng 2; . B. Hàm số fx nghịch biến trên khoảng 1;1 . C. Hàm số fx đồng biến trên khoảng 2;1 . D. Hàm số fx nghịch biến trên khoảng ;2 Lời giải Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 72 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 126. Cho hàm số y f x xác định, liên tục trên và có đạo hàm fx . Biết rằng fx có đồ thị như hình vẽ bên. Mệnh đề nào sau đây đúng? A. Hàm số y f x đồng biến trên khoảng 2;0 . B. Hàm số y f x nghịch biến trên khoảng 0; . C. Hàm số y f x đồng biến trên khoảng ;3 . D. Hàm số y f x nghịch biến trên khoảng 3; 2 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 127. Cho hàm số y f x có đao hàm fx xác định, liên tục trên có đồ thị fx như hình vẽ bên. Khẳng định nào sau đây là đúng ? A. Hàm số y f x đồng biến trên khoảng 1; . B. Hàm số y f x đồng biến trên khoảng ;1 và 3; . C. Hàm số y f x nghịch biến trên khoảng ;1 . D. Hàm số y f x đồng biến trên khoảng 1;3 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 73 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 128. Cho hàm số y f x . Biết hàm số ' y f x có đồ thị như hình vẽ bên. Hàm số 14 g x f x đồng biến trên khoảng nào dưới đây? A. 1;0 . B. ;0 . C. 1 ;0 4 . D. 1 ; 4 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 129. Cho hàm số y f x có đạo hàm trên . Hàm số '( ) y f x có đồ thị như hình vẽ bên. Xét hàm số ( ) (1 ) y g x f x . Mệnh đề nào sau đây là đúng? A. Hàm số y g x đồng biến trên khoảng (4; ) B. Hàm số y g x đồng biến trên khoảng 1;1 . C. Hàm số y g x nghịch biến trên khoảng ( ;0) D. Hàm số y g x nghịch biến trên khoảng 0;2 Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 74 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 130. Cho hàm số y f x liên tục trên và có bảng xét dấu fx như sau: Đặt hàm số 11 y g x f x . Mệnh đề nào sau đây về hàm số y g x là đúng? A. Hàm số đồng biến trên khoảng ;2 . B. Hàm số nghịch biến biến trên khoảng 2;1 . C. Hàm số đồng biến trên khoảng 2; . D. Hàm số nghịch biến trên khoảng 1; . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 131. Cho hàm số y f x liên tục trên và có bảng biến thiên như sau. Đặt hàm số 22 y g x f x Mệnh đề nào sau đây là đúng? A. Hàm số y g x đồng biến trên khoảng ;1 . B. Hàm số y g x nghịch biến trên khoảng 0;2 C. Hàm số y g x đồng biến trên khoảng 2; . D. Hàm số y g x nghịch biến trên khoảng ;0 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 75 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 132. Cho hàm số () y f x có đạo hàm trên . Hàm số () y f x có đồ thị như hình vẽ bên. Hàm số 2 y f x đồng biến trên khoảng nào dưới đây: A. 1;2 . B. 1; . C. 2; 1 . D. 1;1 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 133. Cho hàm số y f x . Hàm số y f x có đồ thị như hình vẽ. Hàm số 2 y f x đồng biến trên khoảng A. 1;2 . B. 1;1 . C. 1; . D. 2; 1 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 76 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 134. Cho hàm số fx . Biết hàm số y f x có đồ thị như hình vẽ bên dưới. Hàm số 2 3 y f x đồng biến trên khoảng. A. 2;3 . B. 2; 1 . C. 0;1 . D. 1;0 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 77 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 135. Cho hàm số fx có đạo hàm liên tục trên và có đồ thị của hàm y f x như hình vẽ. Xét hàm số 2 ( ) 2 g x f x . Mệnh đề nào dưới đây sai? A. Hàm số () gx đồng biến trên 2; . B. Hàm số () gx nghịch biến trên 0;2 . C. Hàm số () gx nghịch biến trên 1;0 . D. Hàm số () gx nghịch biến trên ; 2 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 136. Cho hàm số y f x có đạo hàm 2 2 ' 9 4 f x x x x . Khi đó hàm số 2 y f x nghịch biến trên khoảng nào dưới đây? A. 2;2 . B. ;3 . C. 3;0 . D. 3; . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 78 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 137. Cho hàm số y f x . Hàm số y f x có đồ thị như hình vẽ bên. Hàm số 2 1 y f x nghịch biến trên khoảng nào dưới đây? A. 3; . B. 3; 1 . C. 1; 3 . D. 0;1 Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 138. Cho hàm số y f x . Biết hàm số ' y f x có đồ thị như hình vẽ bên. Hàm số 2 23 y f x x đồng biến trên khoảng nào dưới đây? A. 11 ; 32 . B. 1 ; 2 . C. 1 ; 3 . D. 1 2; 2 . Lời giải x y 4 2 O 1 Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 79 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 139. Cho hàm số y f x có đạo hàm trên . Hàm số y f x có đồ thị như hình vẽ bên. Đặt y g x f x x . Khẳng định nào sau đây về hàm số y g x là đúng? A. Hàm số đồng biến trên khoảng 1;2 . B. Hàm số nghịch biến trên khoảng 2; . C. Hàm số đồng biến trên khoảng 1;1 . D. Hàm số nghịch biến trên khoảng 1;2 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 80 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 140. Cho hàm số y f x có đạo hàm trên . Hàm số y f x có đồ thị như hình vẽ bên. Đặt 2 21 y g x f x x . Khẳng định nào sau đây về hàm số y g x là đúng? A. Hàm số nghịch biến trên khoảng ;3 . B. Hàm số nghịch biến trên khoảng 3;1 . C. Hàm số nghịch biến trên khoảng 3; . D. Hàm số nghịch biến trên khoảng 1;3 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 141. Cho hàm số y f x có đạo hàm trên . Hàm số y f x có đồ thị như hình vẽ bên. Đặt 2 1 1 2 y g x f x x x . Khẳng định nào sau đây về hàm số y g x là đúng? A. Hàm số đồng biến trên khoảng 1;3 . B. Hàm số nghịch biến trên khoảng ;3 . C. Hàm số đồng biến trên khoảng 3; . D. Hàm số đồng biến trên khoảng 3; 1 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 81 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 142. Cho hàm số y f x có đạo hàm trên . Hàm số y f x có đồ thị như hình vẽ bên. Đặt 2 2 x y g x f x . Khẳng định nào sau đây về hàm số y g x là sai? A. Hàm số đồng biến trên khoảng 1;1 . B. Hàm số nghịch biến trên khoảng ;1 . C. Hàm số đồng biến trên khoảng 2; . D. Hàm số nghịch biến trên khoảng 1;2 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 143. Cho hàm số y f x có đạo hàm trên . Hàm số y f x có đồ thị như hình vẽ bên. Đặt 3 2 1 3 x y g x f x x x . Khẳng định nào sau đây về hàm số y g x là đúng? A. Hàm số đồng biến trên khoảng ;0 . B. Hàm số nghịch biến trên khoảng 0;1 . C. Hàm số đồng biến trên khoảng 2; . D. Hàm số đồng biến trên khoảng 1;2 . Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 82 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 144. Cho hàm số y f x có đạo hàm trên . Đồ thị của hàm số y f x như hình vẽ bên. Hàm số 32 1 3 3 1 3 4 2 y g x f x x x x . Mệnh đề nào dưới đây về hàm số y g x là sai? A. Hàm số nghịch biến trên khoảng ;3 . B. Hàm số nghịch biến trên khoảng 3; 1 . C. Hàm số đồng biến trên khoảng 1;1 D. Hàm số nghịch biến trên khoảng 1; . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 83 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 Câu 145. Cho hàm số fx có đạo hàm liên tục trên Bảng biến thiên y f x được cho như sau: Hàm số 1 2 x y f x nghịch biến trên khoảng nào dưới đây A. 2;4 . B. 0;2 . C. 2;0 . D. 4; 2 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 146. Cho hàm số y f x xác định trên và có đồ thị fx như hình vẽ dưới đây: Hàm số 2 1 2 x y g x f x x nghịch biến trên khoảng A. 3;1 . B. 2;0 . C. 1;3 . D. 3 1; 2 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. x y 3 -2 3 2 -1 1 -2 5 O Trung Tâm Luyện Thi Đại Học Amsterdam Chương I-Bài 1. Tính Đơn Điệu Của Hàm Số 84 Lớp Toán Thầy-Diệp Tuân Tel: 0935.660.880 .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 147. Cho hàm số y f x xác định trên và fx thỏa 1 2 1 f x x x g x , trong đó 0 gx với mọi x . Hàm số 12 y f x x nghịch biến trên khoảng nào? A. 1; . B. 0;3 . C. ;3 . D. 3; Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. Câu 148. Cho hàm số y f x có đạo hàm trên sao cho 21 f , 20 f . Hàm số y f x có đồ thị như hình vẽ dưới. Hàm số 2 y f x nghịch biến trên khoảng nào trong các khoảng sau? A. 3 1; 2 . B. 2; 1 . C. 1;1 . D. 1; 2 . Lời giải .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. .............................................................................................. .................................................................................................... .................................................................................................... .................................................................................................... .................................................................................................... .............................................................................................. .............................................................................................. .............................................................................................. ..............................................................................................