What is the absolute maximum value of $f(x)=x^3-3x+1$ on $[-2,2]$?

Core Concept

$f'(x)=3x^2-3$ gives critical points $x=\pm 1$. The candidates are $f(-2)=-1$, $f(-1)=3$, $f(1)=-1$, and $f(2)=3$, so the maximum value is $3$.