In this lesson, we learn about finding extreme values on intervals. We start by recalling the extreme value theorem, which states that a continuous function on a closed bounded interval attains a minimum and a maximum value. We then discuss how to find the minimum and maximum values of a function on a closed bounded interval by first finding all the critical points in the interior of the interval and then computing the values of F at the critical points and at the end points of the interval. We also learn about one-sided derivatives at end points and their role in determining end point extrema. Finally, we discuss the role of the second derivative in finding extreme values on open intervals by stating the second derivative test.
Global (absolute) maximum and minimum values on closed intervals. Endpoint (one-sided) derivatives. The second derivative and extrema on open intervals.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.