Problem:
Find the maximum value of $f(x) = x^3-3x$ on the set of all real numbers $x$ satisfying $x^4+36 \le 13x^2$.
I made a graph of $f(x)$ (but I don't know how to show it here).
I know that the solution set of the inequality is $-3\le x \le -2$ and $2 \le x \le 3$, but after that I am a bit lost.
Do I just plug in the value of those solution sets of the inequality to find which one is largest for $f(x)$?