Find the interval(s) on which $f(x) = x^{3} - 3 x^{2} - 9 x + 5$ is strictly decreasing.

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

3. 03

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