Find the interval(s) on which $f(x) = x^{3} + 3 x^{2} - 24 x + 1$ is strictly increasing.

Explanation

1. 01

   $f'(x) = 3 \left(x - 2\right) \left(x + 4\right)$, which is 0 at $x = -4, 2$.

2. 02

   $f'(x) > 0$ on $(-\infty, -4) \cup (2, \infty)$ and $f'(x) < 0$ on $(-4, 2)$.

3. 03

   So $f$ is strictly increasing on $(-\infty, -4) \cup (2, \infty)$.