### 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