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Grade 5-12

Mean Value Theorem - Tricky Toll Booth Ticket

by Robert Abramovic | Science

6 Lessons 52:00
  1. 1. The Speed Limits at the Tollbooths 6:46
  2. 2. Your Drive on the Highway 4:20
  3. 3. Why Did You Get a Speeding Ticket 5:57
  4. 4. Continuous Functions Defined 11:58
  5. 5. Review of the Instantaneous Rate of Change and the Average Rate of Change 11:54
  6. 6. The Mean Value Theorem 11:05

Grade 5-12



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.


  • Average Rate of Change
  • Average Speed
  • Average Velocity
  • Continuous Functions
  • Instantaneous Rate of Change
  • Kinematics
  • Mathematics
  • Mean Value Theorem
  • The Derivative


Hi, I'm Robert. I hold a Ph.D. in Mathematics as well as a BA in Physics. I have been a private tutor for over 13 years. I enjoying sharing my knowledge of mathematics and physics with students, creating relatable examples, and making learning fun. My philosophy is not only teaching students but inspiring them to learn more about the material on their own.

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