a) A = 5x - x² = - ( x² - 2.x.$\frac{5}{2}$ + $\frac{25}{4}$ - $\frac{25}{4}$ ) = $\frac{25}{4}$ - ( x - $\frac{5}{2}$ )² ≤ $\frac{25}{4}$
Dấu " = " xảy ra khi x - $\frac{5}{2}$ = 0 ⇔ x = $\frac{5}{2}$
Vậy Max A = $\frac{25}{4}$ khi x = $\frac{5}{2}$
b) B = x - x² = - ( x² - 2.x.$\frac{1}{2}$ + $\frac{1}{4}$ - $\frac{1}{4}$ ) = $\frac{1}{4}$ - ( x - $\frac{1}{2}$ )² ≤ $\frac{1}{4}$
Dấu " = " xảy ra khi x - $\frac{1}{2}$ = 0 ⇔ x = $\frac{1}{2}$
Vậy Max B = $\frac{1}{4}$ khi x = $\frac{1}{2}$
c) C = 4x - x² + 3 = - ( x² - 4x - 3 ) = - ( x² - 4x + 4 - 7 ) = 7 - ( x - 2 )² ≤ 7
Dấu " = " xảy ra khi x - 2 = 0 ⇔ x = 2
Vậy Max C = 7 khi x = 2
