What is the local maximum value of $f(x) = x^{3} - 12 x + 5$?

Explanation

1. 01

   $f'(x) = 3 \left(x - 2\right) \left(x + 2\right) = 0$ at $x = -2$ and $x = 2$.

2. 02

   $f''(x) = 6 x$: $f''(-2) = -12$, so $x = -2$ is a local maximum.

3. 03

   The value there is $f(-2) = 21$.