Fermat's Theorem on Stationary Points
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Fermat's theorem on stationary points states that if is a local extremum in the interval and is differentiable at , then .
Contributed by: Julio Cesar de la Yncera (March 2011)
Open content licensed under CC BY-NC-SA
Snapshot 1: a local maximum; notice the slope is zero
Snapshot 2: a local minimum; the slope is also zero here; also notice the change of sign from positive to negative for the maximum and from negative slope to positive slope for the minimum
"Fermat's Theorem on Stationary Points"
Wolfram Demonstrations Project
Published: March 7 2011