# Find the interval in which $y=x^2e^{-x}$ is increasing.

Toolbox:
• For increasing $f ' (x) \geq 0$
• For decreasing $f ' (x) \leq 0$
Step 1
$\large\frac{dy}{dx} = 2x\: e^{-x}-x^2e^{-x}=0$
$\Rightarrow x = 0, \: 2$
$f(x)$ is increasing in [ 0 2 ]
in $( -\infty, \: 0]\: \cup \: [2\: \infty)\: f(x)$ is decreasing