2.10 The Mean Value Theorem

By the end of your studying, you should know:
Onscreen applet instructions:
The tangent line, when you find it, will be solid and not dotted.
ExamplesAt 7 p.m., a car is traveling at 50 miles per hour. Ten minutes later, the car has slowed to 30 miles per hour. Show that at some time between 7 and 7:10 the car's acceleration is exactly 120, in units of miles per hours squared.At a particular horse race, two horses start at the same time, and finish in a tie. Show that at some time during the race, the horses were running at the same speed.
Suppose f is a differentiable function such that
AppletsMean Value Theorem
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 2.10 The Mean Value Theorem (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications
Mean Value Theorem

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2.9 Derivatives of the Trigonometric Functions  Table of Contents  2.11 Implicit Differentiation 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel