Extreme Values on Intervals
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.
- Endpoint and Absolute Extreme Values - Practice with Endpoint and Absolute Extreme Values.
- How do you find extreme values of a function?
- How do you find the minimum and maximum values on a closed, bounded interval?
- How do you find a one-sided derivative at an endpoint of a function on an interval?
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Staff Review
The extreme value theorem is reviewed to begin this lesson. You will then learn how to find the minimum and maximum values of a function on a closed, bounded interval. Several useful theorems and results are discussed that deal with extreme values at endpoints. There are some good example problems as well. -
Dierdre
Very detailed explanations and he speaks slowly and clearly enough for students to follow. Also, there are pictures provided for those students who are visual.
