What is the local maximum value of $f(x) = - 2 x^{3} + 9 x^{2} - 12 x + 7$?

Explanation

1. 01

   $f'(x) = - 6 \left(x - 2\right) \left(x - 1\right) = 0$ at $x = 1$ and $x = 2$.

2. 02

   $f''(x) = 18 - 12 x$: $f''(2) = -6$, so $x = 2$ is a local maximum.

3. 03

   The value there is $f(2) = 3$.