### Overview

The mean value theorem tells us (roughly) that if we know the slope of the secant line of a function whose derivative is continuous, then there must be a tangent line nearby with that same slope. This lets us draw conclusions about the behavior of a function based on knowledge of its derivative.

### Lecture Video and Notes

#### Video Excerpts

Clip 1: Description of the Mean Value Theorem

Clip 2: Consequences of the Mean Value Theorem

### Recitation Video

#### Increasing or Decreasing

### Worked Example

Generalizing the Mean Value Theorem