Session 35: Using the Mean Value Theorem

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Overview

We can use the mean value theorem to prove that linear approximations do, in fact, provide good approximations of a function on a small interval. The information the theorem gives us about the derivative of a function can also be used to find lower or upper bounds on the values of that function.

Lecture Video and Notes

Video Excerpts

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» Clip 1: The Mean Value Theorem and Linear Approximation (00:08:00)

» Accompanying Notes (PDF)

From Lecture 14 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: The Mean Value Theorem and Inequalities (00:07:00)

» Accompanying Notes (PDF)

From Lecture 14 of 18.01 Single Variable Calculus, Fall 2006

Worked Example

 

The Mean Value Theorem and the Sine Function

Recitation Video

 

Comparing Functions Using the MVT

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Derivative With a Discontinuity

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