Interactive: Fermat's Theorem

Fermat's Theorem: If \(f\) is a local maximum or minimum at \(c\), and if \(f'(c)\) exists, then \(f'(c)=0\).

Critical Number: A number \(c\) in the domain of \(f\) such that either \(f'(c)=0\) or \(f'(c)\) does not exist.

Instructions: With the mouse, move point P along the function and you will see it's derivative traced in green. Here c and d are the critical numbers for the function graphed in blue. Refresh browser to start over.