Definition of the Mean Value Theorem

A detailed tutorial on the solving of the Mean Value Theorem. Step by step tutorial including several examples of how to solve the Mean Value Theorem for reference.

 Overview

You can easily figure out what the Mean Value Theorem is by looking at the word mean – a mean is an average. The Mean Value Theorem states that there is at least one point on the graph of a function where the derivative is equal to the average slope of the entire section of the graph you are looking at. The requirements are that the graph is both continuous and differentiable on the interval [a, b], where a < b. Then there exists some c in (a, b) such that:

 f ‘(c) = [f(b) - f(a)] / [b - a]

The Mean Value Theorem is very similar to Rolle’s Theorem, which is a more specific theorem stating the same thing.

Bookmark It

Hide Sites