3 2 Rolles THM and the Mean Value

3. 2 Rolle’s THM and the Mean Value THM Review:

3. 2 Rolle’s THM and the Mean Value THM Review: Both of these values can occur at the endpoints. Rolle’s THM gives conditions that guarantee the existence of an extreme value in the interior of a closed interval.

Example

3. 2 Rolle’s THM and the Mean Value THM Rolle’s THM

3. 2 Rolle’s THM and the Mean Value THM

THM 3. 4 The Mean Value THM Last Problem

3. 2 Rolle’s THM and the Mean Value THM

3. 2 Rolle’s THM and the Mean Value THM

3. 2 Rolle’s THM and the Mean Value THM

Two stationary patrol cars equipped with radar are 5 miles apart on a highway. As a truck passes the first patrol car, its speed is 55 mph. Four minutes later, when the truck passes the second patrol car, its speed is 50 mph. Prove that the truck must have exceeded the speed limit (of 55 mph) at some time during the four minutes. Work

3. 2 Rolle’s THM and the Mean Value THM Convert Time to Hours Question

3. 2 Rolle’s THM and the Mean Value THM Alternative form of the mean value THM Note: When working the exercises for this section, keep in mind that • Polynomial Functions • Rational Functions • Trig Functions Are differentiable at all points in their domains

3. 2 Rolle’s THM and the Mean Value THM HW Section 3. 2, pp. 167 -168 1 -45 odd