` 1) ` ` A = -x^2 + 4x - 10 `
` A = -(x^2 - 4x + 4) - 6 `
` A = -(x - 2)^2 - 6 `
Vì ` -(x - 2)^2 ≤ 0 `
` => -(x - 2)^2 - 6 ≤ -6 `
` => A ≤ -6 `
Vậy ` Max_A = -6, ` dấu $"="$ xảy ra khi: ` x - 2 = 0 <=> x = 2 `
` 2) ` ` B = -x^2 + x `
` B = -(x^2 - x + 1/4) + 1/4 `
` B = -(x - 1/2)^2 + 1/4 `
Vì ` -(x - 1/2)^2 ≤ 0 `
` => -(x - 1/2)^2 + 1/4 ≤ 1/4 `
` => B ≤ 1/4 `
Vậy ` Max_B = 1/4 , ` dấu $"="$ xảy ra khi: ` x - 1/2 = 0 <=> x = 1/2 `
` 3) ` ` C = 4\sqrt{x} - x + 5 `
` C = -(x - 4\sqrt{x} + 4) + 9 `
` C = -(\sqrt{x} - 2)^2 + 9 `
Vì ` -(\sqrt{x} - 2)^2 ≤ 0 `
` => -(\sqrt{x} - 2)^2 + 9 ≤ 9 `
` => C ≤ 9 `
Vậy ` Max_C = 9 , ` dấu $"="$ xảy ra khi: ` \sqrt{x} - 2 = 0 <=> x = 4 `
` 4) ` ` D = 6\sqrt{x} - x + 8 `
` D = -(x - 6\sqrt{x} + 9) + 17 `
` D = -(\sqrt{x} - 3)^2 + 17 `
Vì ` -(\sqrt{x} - 3)^2 ≤ 0 `
` => -(\sqrt{x} - 3)^2 + 17 ≤ 17 `
` => D ≤ 17 `
Vậy ` Max_D = 17, ` dấu $"="$ xảy ra khi: ` \sqrt{x} - 3 = 0 <=> x = 9 `
