Learning Outcomes
 Understand the meaning of Rolle’s theorem.
 Understand the meaning of the Mean Value Theorem
 Verify that the Mean Value Theorem applies and find values guaranteed by the Mean Value Theorem.
 State three important consequences of the Mean Value Theorem.
Textbook
 Chapter 4.4 The Mean Value Theorem
Textbook Assignment
 p. 388: 161, 164, 168, 171, 174, 186, 188
WeBWork Assignment
 ApplicationMean Value Theorem
Exit problems of the session

Determine whether the Mean Value Theorem applies for the following functions over the given interval . If yes, then find that satisfies the Mean Value Theorem.
(a). over (b). over
Key Concepts
 Rolle’s Theorem: If is continuous over and differentiable over , and , then there exist a point , such that .
 The Mean Value Theorem: If is continuous over and differentiable over , then there exist a point , such that
 Three important corollaries of the Mean Value Theorem:
 If over an interval I, then is constant over I.
 If two differentiable functions and satisfy over I, then for some constant .
 If over an interval I, then is increasing over I. If over an interval I, then is decreasing over I.
Videos and Practice Problems of Selected Topics
 The Mean Value Theorem (6:36) The statement and what it means geometrically.
 A polynomial example (4:49) Given and the interval , find satisfying the Mean Value Theorem.
 A square root function example (6:23) Given and the interval , find satisfying the Mean Value Theorem.
 * Practice: Using the Mean Value Theorem. (4 problems)