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
» Clip 1: The Mean Value Theorem and Linear Approximation (00:08:00)
From Lecture 14 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: The Mean Value Theorem and Linear Approximation
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» Clip 2: The Mean Value Theorem and Inequalities (00:07:00)
From Lecture 14 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: The Mean Value Theorem and Inequalities
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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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