Find the interval(s) on which $f(x) = - 2 x^{3} + 15 x^{2} - 36 x + 1$ is strictly decreasing.

Explanation

1. 01

   $f'(x) = - 6 x^{2} + 30 x - 36 = - 6 \left(x - 3\right) \left(x - 2\right)$, which is 0 at $x = 2$ and $x = 3$.

2. 02

   $f'(x) > 0$ on $(2, 3)$ and $f'(x) < 0$ on $(-\infty, 2) \cup (3, \infty)$.

3. 03

   So $f$ is strictly decreasing on $(-\infty, 2) \cup (3, \infty)$.