What is the greatest value of $f(x) = x^{4} - 2 x^{2} + 5$ on $[-2, 1]$?

Explanation

1. 01

   Critical points inside the interval: $f'(x) = 4 x \left(x - 1\right) \left(x + 1\right) = 0$ at $x = -1, 0$.

2. 02

   Compare $f$ there and at the two ends: $f(-2) = 13$, $f(1) = 4$, $f(-1) = 4$, $f(0) = 5$.

3. 03

   The greatest value is $13$, at an end of the interval.