Lesson: The Mean Value Theorem Mathematics • Higher Education

In this lesson, we will learn how to interpret and use the mean value theorem.

Lesson Plan

Students will be able to

understand how Rolle’s theorem relates to the mean value theorem,
understand the mean value theorem and when its conditions are satisfied,
find points in an interval that satisfy the mean value theorem for a given function.

Lesson Video

Lesson Worksheet

Q1:

Mason is not convinced that the mean value theorem is true because, he says, the function has the property that if we take and , we have , and yet there is no point where . What is his error?

Q2:

Madison is not convinced that the mean value theorem is true because, she says, the function is certainly differentiable on . But if we take and , we have , and yet there is no point where . What is her error?

Q3:

Does the mean value theorem apply for the function over the interval ?