Read Section 5.1 (pages 103-106). Fermat's Theorem indicates how derivatives can be used to find where a function attains its highest or lowest points.
Watch this video from 30:00 to the end. The lecture will make use of the first and second derivative tests, which you will read about below.
Work through problems 1-12 and 15 for Exercise 5.1. When you are done, check your answers against Appendix A.