The Mean-Value Theorem and Related Results
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Lesson Description:
Rolle's theorem and the mean-value theorem. Invervals where a function is increasing/decreasing/constant.
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.
Additional Resources:
- The Mean Value Theorem - Practice with The Mean Value Theorem.
Questions answered by this video:
- What is the mean-value theorem?
- What is the extreme value theorem?
- What is Rolle's theorem?
- How do you prove the mean-value theorem?
- What does it mean for a function to be increasing, decreasing, or constant on an interval?
- What is the interior of an interval?
- How can you tell when a function is increasing, decreasing, or constant?
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Staff Review
The mean value theorem, extreme value theorem, Rolleâs theorem, and other important results are defined and explained. They are defined using high-level terminology and intended for students who have a good understanding of math terminology. Some of the definitions may be difficult for the beginning Calculus student to understand. This lecture could be particularly useful to an Analysis student. This lesson is completely packed full of material. It is very useful, and also somewhat overwhelming at times.
