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.

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P

c

d