A function has $f'(x) = x^{2} \left(x + 2\right)$. Find the interval(s) on which $f$ is strictly increasing.

Explanation

1. 01

   $x^{2} \ge 0$ always, so the sign of $f'$ is the sign of $x + 2$.

2. 02

   $f' > 0$ for $x > -2$ except at $x = 0$, where it is 0 for an instant; a single such point does not stop $f$ from strictly increasing.

3. 03

   So $f$ is strictly increasing on $(-2, \infty)$.