GeoGebra Classroom

Mean Value Theorem: Quick Intuitive Tests

John went on the entrance ramp of a highway. The overhead highway radar detected he got on the highway at 12:38PM. He drove for a bit, and the overhead radar on the exit ramp detected he got off the highway at 12:55PM. In this time, he drove a total distance of 30 miles. During his travel time, he never drove under an overhead speed detector. Yet 2 weeks later, John got a speeding ticket in the mail. The ticket claimed he was speeding in great excess over the allotted speed limit of 70 mi/hr. Even though no law enforcement officer ever saw John traveling, does the state police department have the right to issue him a ticket?

Select all that apply
• A
• B

Explain why (in a way that someone who has not taken calculus would understand).

Describe the Mean Value Theorem in your own words. As you do, consider the following: What criterion/criteria does it require? If all sufficient criteria do hold true, what does it allow us to conclude?

In each applet below, the line passing through C is tangent to the graph of this function. Also note the secant segment displayed.