Find the interval(s) on which $f(x) = - x^{3} + 3 x^{2} + 9 x - 2$ is strictly increasing.

Explanation

1. 01

   $f'(x) = - 3 x^{2} + 6 x + 9 = - 3 \left(x - 3\right) \left(x + 1\right)$, which is 0 at $x = -1$ and $x = 3$.

2. 02

   $f'(x) > 0$ on $(-1, 3)$ and $f'(x) < 0$ on $(-\infty, -1) \cup (3, \infty)$.

3. 03

   So $f$ is strictly increasing on $(-1, 3)$.