Tìm giá trị lớn nhất A= -3x(x+3)-7 B= -2x^2 +5x-8 C=3-x^2+4x Gỉai chi tiết nhé

thuyduonginte

2 năm trước

Loga Sinh Học lớp 12

0 lượt thích 18 xem

1 trả lời

Thích Trả lời

Nguyentuquyen2000

Đáp án+Giải thích các bước giải:

$A=-3x(x+3)-7$
$A=-3x^2-9x-7$
$A=-3x^2-9x-\dfrac{27}{4}-\dfrac{1}{4}$
$A=-3(x^2+3x+\dfrac{9}{4})-\dfrac{1}{4}$
$A=-3(x+\dfrac{3}{2})^2-\dfrac{1}{4}$

$-3(x+\dfrac{3}{2})^2≤0∀x$
$⇔-3(x+\dfrac{3}{2})^2-\dfrac{1}{4}≤\dfrac{-1}{4}$
Dấu $"="$ xảy ra khi $x+\dfrac{3}{2}=0⇔x=\dfrac{-3}{2}$
Vậy $A_{max}=\dfrac{-1}{4}⇔x=\dfrac{-3}{2}$

----------------------------------------

$B=-2x^2+5x-8$
$B=-2x^2+5x-\dfrac{25}{8}-\dfrac{39}{8}$
$B=-2(x^2-\dfrac{5}{2}x+\dfrac{25}{16})-\dfrac{39}{18}$

$B=-2(x-\dfrac{5}{4})^2-\dfrac{39}{18}$
$-2(x-\dfrac{5}{4})^2≤0∀x$
$⇔-2(x-\dfrac{5}{4})^2-\dfrac{39}{18}≤\dfrac{-39}{18}$
Dấu $"="$ xảy ra khi $x-\dfrac{5}{4}=0⇔x=\dfrac{5}{4}$
Vậy $B_{max}=\dfrac{-39}{18}⇔x=\dfrac{5}{4}$
-----------------------------------

$C=3-x^2+4x$
$C=-x^2+4x-4+7$

$C=-(x^2-4x+4)+7$
$C=-(x-2)^2+7$
$-(x-2)^2≤0∀x$
$⇔-(x-2)^2+7≤7$
Dấu $"="$ xảy ra khi $x-2=0⇔x=2$
Vậy $C_{max}=7⇔x=2$

Vote (0) Phản hồi (0) 2 năm trước

lufy84socute2

`A = -3x(x + 3) - 7 = -3x^2 - 9x - 7`

`= -3(x^2 + 3x) - 7 = -3(x^2 + 3x + 9/4) - 7 + 27/4`

`= -3(x + 3/2)^2 - 1/4 <= -1/4 ∀ x ∈ R`

Dấu ''='' xảy ra `<=> x + 3/2 = 0 <=> x = -3/2`

Vậy `maxA = -1/4 <=> x = -3/2`

`B = -2x^2 + 5x - 8 = -2(x^2 - 5/2x) - 8`

`= -2(x^2 - 5/2x + 25/16) - 8 + 25/8`

`= -2(x - 5/2)^2 -39/8 <= -39/8 ∀ x ∈ R`

Dấu ''='' xảy ra `<=> x - 5/2 = 2 <=> x = 5/2`

Vậy `maxB = -39/8 <=> x = 5/2`

`C = 3 - x^2 + 4x = -x^2 + 4x + 3 = -(x^2 - 4x) + 3`

`= -(x^2 - 4x + 4) + 3 + 4`

`= -(x - 2)^2 + 7 <= 7 ∀ x ∈ R`

Dấu ''='' xảy ra `<=> x - 2 = 0 <=> x = 2`

Vậy `maxC = 7 <=> x = 2`

Vote (0) Phản hồi (0) 2 năm trước

Các câu hỏi liên quan

Bài 11: Join each pair of sentences by using a conjunction: and, but, or, so. 1. The bus stopped. The man got off. 2. Junk food tastes so good. It is bad for your health. 3. You should eat less junk food. You will put on weight. 4. He is a vegetarian. He doesn’t eat any meat. 5. Would you like meat for lunch? Would you like vegetables for lunch? 6. Susan went to the park. She had a ride on the swing. 7. I love fruit. I am allergic to strawberries. 8. There was a heavy rain. The roads were flooded. Bài 12: Arrange the words to make sentences. 1. cold/ I/ sore throat/ love/ a/ drinks/ but/ have/ I. 2. Jim/ overweight/ so/ eats/ is/ fast food/ too much/ he. 3. too much/ bad/ television/ watching/ for/ health/ your/ is? 4. the flu/ should/ you/ a cold/ if/ have/ or/ you/ home/ stay. 5. Alex/ usually/ fishing/ so/ loves/ goes/ in/ near/ he/ his house/ fishing/ the lake. 6. you/ some/ clean/ yourself/ avoid/ diseases/ by/ can/ keeping.

Xin mời các cao nhân.....................................

a,4^8:4^5-(1^30+17):3^2 b,4.5^2-3.2^3 c,150-[10^2-(14-11)^2.2007] d,15.2^3+4.3-5.7 e,3^3.118-3^3.18 f,12:{390:[500-(125+35.7)]}

Giúppp ! Thật sự thì mik quên cách lm rùi ;-;

Bài 10: Fill in the blanks with and,so, but, or. 1. We stayed at home ________ watched a film. 2. I want to buy a new car, ________ I don’t have enough money. 3. She had a terrible headache last night, ________ she couldn’t go out. 4. I eat cake, ________ I never eat biscuits; I don’t like them. 5. Would you like cake ________ biscuits with your coffee? 6. My job is very interesting, ________ it doesn’t pay very well. 7. We can go by bus, ________ we can walk. 8. My classmate studies very hard, ________ she always gets good marks. 9. You had better hurry up, ________ you’ll be late for work. 10. The Japanese eat healthily, ________ they have high life expectancy.

cô pé dốt toán siu cấp super ultra lại típ tục không biết làm bài, mn giúp cô pé zới T T

helpppppppppppppppppppppppppppppppppp

Tìm nghiệm nguyên phương trình x^2 −2xy+x−y+1=0

cali : tên khánh linh đổ bóng trng trí đơn giản ko màu mè ( nếu đc ghép thêm ảnh cô gái tóc ngắn giản dị )

Số sánh không quy đồng tử hoặc mẫu 5/8 và 7/12

Loga.vn - Cộng Đồng Luyện Thi Trực Tuyến