Find the interval(s) on which $f(x) = x^{3} - 27 x + 2$ is strictly decreasing.

Explanation

1. 01

   $f'(x) = 3 x^{2} - 27 = 3 \left(x - 3\right) \left(x + 3\right)$, which is 0 at $x = -3$ and $x = 3$.

2. 02

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

3. 03

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