B = x - x² + 6
= -x² + x - $\frac{1}{4}$ + $\frac{25}{4}$
= -(x² - x + $\frac{1}{4}$) + $\frac{25}{4}$
= -(x - $\frac{1}{2}$)² + $\frac{25}{4}$
Có: (x - $\frac{1}{2}$)² ≥ 0 với mọi x
⇒ -(x - $\frac{1}{2}$)² ≤ 0
⇒ -(x - $\frac{1}{2}$)² + $\frac{25}{4}$ ≤ $\frac{25}{4}$
⇒ B ≤ $\frac{25}{4}$
Dấu "=" xảy ra ⇔ x - $\frac{1}{2}$ = 0
⇔ x = $\frac{1}{2}$
Vậy B max = $\frac{25}{4}$ khi x = $\frac{1}{2}$
