tìm gltn và gtnn của hàm số y=3 \cos x+2

y= 3cosx+2 

Ta có :

$-1 \leq \cos x \leq 1$
$\Rightarrow-3 \leq 3 \cos x \leq 3$
$\Rightarrow-1 \leq 3 \cos x+2 \leq 5$
$\Rightarrow-1 \leq y \leq 5$

$\Rightarrow \max \mathrm{y}=6 \Leftrightarrow \sin 3 \mathrm{x}=-1 \Rightarrow \mathrm{x}=\frac{-\pi}{6}+\frac{\mathrm{k} 2 \pi}{3}, \mathrm{k} \in \mathbb{Z}$
$\Rightarrow \min \mathrm{y}=-4 \Leftrightarrow \sin 3 \mathrm{x}=1 \Rightarrow \mathrm{x}=\frac{\pi}{6}+\frac{\mathrm{k} 2 \pi}{3}, \mathrm{k} \in \mathbb{Z}$