# Mean value theorem review

Review your knowledge of the mean value theorem and use it to solve problems.

## What is the mean value theorem?

The mean value theorem connects the average rate of change of a function to its derivative. It says that for any differentiable function $f$ and an interval $[a,b]$ (within the domain of $f$), there exists a number $c$ within $(a,b)$ such that $f'(c)$ is equal to the function's average rate of change over $[a,b]$.
Graphically, the theorem says that for any arc between two endpoints, there's a point at which the tangent to the arc is parallel to the secant through its endpoints.
Want to learn more about the mean value theorem? Check out this video.

## Check your understanding

Want to try more problems like this? Check out this exercise.