Find the interval(s) on which $f(x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5$ is strictly decreasing.

Explanation

1. 01

   $f'(x) = 12 x \left(x - 2\right) \left(x + 1\right)$, which is 0 at $x = -1, 0, 2$.

2. 02

   Testing the sign between these points, $f'(x) < 0$ on $(-\infty, -1) \cup (0, 2)$.