Derivative test

Graph of a function and its derivative, illustrating how the sign of the derivative identifies local maximum and minimum points.
A graph illustrating the derivative test

In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information about the concavity of a function.

The usefulness of derivatives to find extrema is proved mathematically by Fermat's theorem of stationary points.

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