Infinitesimal calculus MOC

Local extrema

Local extrema are either local minima or local maxima. Every extremum is a Critical point, but not the converse.

Put simply, a point is a local minimum of a function iff. all points in the immediate neighbourhood are greater, and vice versa for maxima. More formally, we say is a local minimum iff.

and a maximum iff.

The absolute extrema are guaranteed to exist for certain functions and domains — see Extreme Value Theorem.

First derivative test

For any critical point , . See Critical point on classifying critical points.

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