Mean Value Theorem Modules
Overview
After completing this section, students should be able to do the following.
- Understand the statement of the Extreme Value Theorem.
- Understand the statement of the Mean Value Theorem.
- Sketch pictures to illustrate why the Mean Value Theorem is true.
- Determine whether Rolle’s Theorem or the Mean Value Theorem can be applied.
- Find the values guaranteed by Rolle’s Theorem or the Mean Value Theorem.
- Use the Mean Value Theorem to solve word problems.
- Compare and contrast the Intermediate Value Theorem, Mean Value Theorem, and Rolle’s Theorem.
- Identify calculus ideas which are consequences of the Mean Value Theorem.
Let's run to class
Ximera Module
Two young mathematicians race to math class.
The Extreme Value Theorem
Ximera Module
We examine a fact about continuous functions.
The Mean Value Theorem
Ximera Module
Here we see a key theorem of calculus.