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Fermat's Theorem on Stationary Points

Fermat's theorem on stationary points states that if is a local extremum in the interval and is differentiable at , then .

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]

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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PERMANENT CITATION

"Fermat's Theorem on Stationary Points" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/FermatsTheoremOnStationaryPoints/
Contributed by: Julio Cesar de la Yncera
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