Editing Maximum and minimum (section)

{{short description|Largest and smallest value taken by a function at a given point}}
{{redirect|Extreme value}}
{{redirect-multi|2|Maximum|Minimum}}
[[File:Extrema example original.svg|thumb|Local and global maxima and minima for cos(3&pi;''x'')/''x'', 0.1&le;'' x ''&le;1.1]]

In [[mathematical analysis]], the '''maximum''' and '''minimum'''{{efn|[[plural|{{sc|pl}}]]: '''maxima''' and '''minima''' (or '''maximums''' and '''minimums''').}} of a [[function (mathematics)|function]] are, respectively, the greatest and least value taken by the function. Known generically as '''extremum''',{{efn|{{sc|pl}}: '''extrema'''.}} they may be defined either within a given [[Interval (mathematics)|range]] (the ''local'' or ''relative'' extrema) or on the entire [[domain of a function|domain]] (the ''global'' or ''absolute'' extrema) of a function.<ref>{{cite book | last=Stewart | first=James | author-link=James Stewart (mathematician) | title=Calculus: Early Transcendentals | publisher=[[Brooks/Cole]] | edition=6th | year=2008 | isbn=978-0-495-01166-8 | url-access=registration | url=https://archive.org/details/calculusearlytra00stew_1 }}</ref><ref>{{cite book | last1=Larson | first1=Ron | author-link=Ron Larson (mathematician)| last2=Edwards | first2=Bruce H. | title=Calculus | publisher=[[Brooks/Cole]] | edition=9th | year=2009 | isbn=978-0-547-16702-2}}</ref><ref>{{cite book | last1 = Thomas | first1 = George B. | last2=Weir | first2= Maurice D. | last3=Hass | first3=Joel |author3-link = Joel Hass| author-link=George B. Thomas | title=Thomas' Calculus: Early Transcendentals | publisher=[[Addison-Wesley]] | year=2010 | edition=12th | isbn=978-0-321-58876-0}}</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 (mathematics)|set]] are the [[greatest and least elements]] in the set, respectively. Unbounded [[infinite set]]s, such as the set of [[real number]]s, have no minimum or maximum.

In [[statistics]], the corresponding concept is the [[sample maximum and minimum]].