## ::Maxima and minima

### ::concepts

''x''::maximum    Function::minimum    Global::point    Local::element    Lowast::''f''    Minima::maxima

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Local and global maxima and minima for cos(3πx)/x, 0.1≤ x ≤1.1

In mathematical analysis, the maxima and minima (the plural of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).<ref>{{#invoke:citation/CS1|citation |CitationClass=book }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=book }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=book }}</ref> Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.

As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum.

Maxima and minima sections
Intro  Definition  Finding functional maxima and minima  Examples  Maxima or minima of a functional   In relation to sets  See also  References  External links

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