What is the least value of $f(x) = - x^{3} + 12 x$ on $[-3, 3]$?

Explanation

1. 01

   Critical points inside the interval: $f'(x) = - 3 \left(x - 2\right) \left(x + 2\right) = 0$ at $x = -2, 2$.

2. 02

   Compare $f$ there and at the two ends: $f(-3) = -9$, $f(3) = 9$, $f(-2) = -16$, $f(2) = 16$.

3. 03

   The least value is $-16$.