$C=-3x^2-9x+2$
$C=-3x^2-9x-\dfrac94+2+\dfrac94$
$C= -3\left(x^2+3x+\dfrac94\right)+\dfrac{17}4$
$C=-3\left(x+\dfrac32\right)^2+\dfrac{17}4$
Vì $-3\left(x+\dfrac32\right)^2\le 0\; \forall x\in \mathbb{R}$
$⇒ -3\left(x+\dfrac32\right)^2+\dfrac{17}4 \le \dfrac{17}4 \; \forall x\in \mathbb{R}$
Vậy $\max =\dfrac{17}4$ khi $x+\dfrac32=0 ⇔ x=-\dfrac32$
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$H=-7x^2+14x-7+4$
$H=-7(x^2-2x+1)+4$
$H=-7(x-1)^2+4$
Vì $-7(x-1)^2\le 0\; \forall x\in \mathbb{R}$
$⇒ -7(x-1)^2+4 \le 4\; \forall x\in \mathbb{R}$
Vậy $\max = 4$ khi $x-1=0 ⇔x=1$
