Written By: Ehsan Jahandarpour

In mathematics, the maximum and minimum (plural: maxima and minima) of a function, known collectively as extrema (singular: extremum), are the largest and smallest value that the function takes at a point either within a given neighborhood (local or relative extremum) or on the function domain in its entirety (global or absolute extremum). Pierre de Fermat was one of the first mathematicians to propose a general technique (called adequality) for finding maxima and minima. More generally, the maximum and minimum of a set (as defined in set theory) are the greatest and least element in the set. Unbounded infinite sets such as the set of real numbers have no minimum and maximum. To locate extreme values is the basic objective of optimization.