What is the greatest value of $f(x) = x^{3} - 3 x$ on $[-2, 3]$?

Explanation

1. 01

   Critical points inside the interval: $f'(x) = 3 \left(x - 1\right) \left(x + 1\right) = 0$ at $x = -1, 1$.

2. 02

   Compare $f$ there and at the two ends: $f(-2) = -2$, $f(3) = 18$, $f(-1) = 2$, $f(1) = -2$.

3. 03

   The greatest value is $18$.