Part C: Mean Value Theorem, Antiderivatives and Differential Equations

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

Clip 1: The Mean Value Theorem and Linear Approximation

Clip 2: The Mean Value Theorem and Inequalities

Worked Example

The Mean Value Theorem and the Sine Function

Recitation Video

Comparing Functions Using the MVT

Derivative With a Discontinuity

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Course Info

Learning Resource Types

grading Exams with Solutions
notes Lecture Notes
theaters Lecture Videos
assignment_turned_in Problem Sets with Solutions
laptop_windows Simulations