Mean Value Theorem - Tricky Toll Booth Ticket

Have you ever wondered why you got a speeding ticket even when no cops were around to watch you exceed the speed limit? Did a camera catch you speeding? Maybe! But another possibility is the mean value theorem! This theorem tells traffic officers that there has to be at least one time when your average speed was equal to your actual speed. If your average speed was over the speed limit, this explains why you got a ticket. In this course, you will embark on a journey on a highway that requires you to drive through two toll-booths: one at the entrance and another at the exit. You will learn how and why you got a speeding ticket as well as the specific mathematical statement of the mean value theorem. Before you learn the statement of the mean value theorem, you will learn about continuous functions and review the average rate of change, and instantaneous rate of change.