Find the interval(s) on which $f(x) = - x^{3} + 6 x^{2} - 9 x + 4$ is strictly increasing.

Explanation

1. 01

   $f'(x) = - 3 \left(x - 3\right) \left(x - 1\right)$, which is 0 at $x = 1, 3$.

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 $(1, 3)$.