Interactive: Mean Value Theorem

Mean Value Theorem: Let \(f\) be a function that satisfies the following:
  • \(f\) is continuous on a closed interval \([a, b]\).
  • \(f\) is differentiable on the open interval \((a,b)\).
Then there is a number \(p\) in \((a,b)\) such that
\[f'\left( p \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}\]

Instructions: With the mouse, move points A and B along the function to see the Mean Value Theorem in action. Refresh browser to start over.

YouTube Video Lectures by Rob Shone