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 .



  • [Snapshot]
  • [Snapshot]


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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