What is the local minimum value of $f(x) = x^{3} - 3 x + 2$?

Explanation

1. 01

   $f'(x) = 3 \left(x - 1\right) \left(x + 1\right) = 0$ at $x = -1$ and $x = 1$.

2. 02

   $f''(x) = 6 x$: $f''(1) = 6$, so $x = 1$ is a local minimum.

3. 03

   The value there is $f(1) = 0$.