Learning Outcomes

1. Understand the meaning of Rolle’s theorem.
2. Understand the meaning of the Mean Value Theorem
3. Verify that the Mean Value Theorem applies and find values guaranteed by the Mean Value Theorem.
4. 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

• Application-Mean Value Theorem

Exit problems of the session

1. 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:
1. If over an interval I, then is constant over I.
2. If two differentiable functions and satisfy over I, then for some constant 3. 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

1. The Mean Value Theorem  (6:36) The statement and what it means geometrically.
2. A polynomial example (4:49) Given and the interval , find satisfying the Mean Value Theorem.
3. A square root function example (6:23) Given and the interval , find satisfying the Mean Value Theorem.
4. * Practice: Using the Mean Value Theorem. (4 problems)