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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

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Details

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

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