Extrema

An extremum (or extreme value in form of maximum and minimum values) of a given function is a point at which it attains a maximum or minimum value. Extrema are important because they provide a lot of information about a function and aid in answering questions of optimality.

Local extremum

A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

absolute extremum

An absolute extremum (or global extremum) of a function in a given interval is the point at which a maximum or minimum value of the function is obtained.


A local minimum of function in is defined as for every in the neighborhood around , where .