Find the interval(s) on which $f(x) = [x(x - 4)]^2$ is strictly increasing.

Explanation

1. 01

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

2. 02

   Testing the sign between these points, $f'(x) > 0$ on $(0, 2) \cup (4, \infty)$.