Chapter 4 - Applications of the Derivative - 4.1 Maxima and Minima - 4.1 Exercises - Page 242: 9

First find all the critical points by seeking all points $x$ in the domain of $f$ so that $f'(x) = 0$ or $f(x)$ doesn’t exist. Now compare the $y$-values of all of these points, together with the $y$-values of the endpoints. The largest $y$-value from among these is the maximum, and the smallest is the minimum.

Follows from definitions.