Find the interval(s) on which $f(x) = x^{2} e^{- x}$ is strictly increasing.

Explanation

1. 01

   $f'(x) = - x \left(x - 2\right) e^{- x}$, which is 0 at $x = 0, 2$.

2. 02

   $f'(x) > 0$ on $(0, 2)$ and $f'(x) < 0$ on $(-\infty, 0) \cup (2, \infty)$.

3. 03

   So $f$ is strictly increasing on $(0, 2)$.