About: Extreme value

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An extreme value, or extremum (plural extrema), is the smallest (minimum) or largest (maximum) value of a function, either in an arbitrarily small neighborhood of a point in the function's domain — in which case it is called a relative or local extremum — or on a given set contained in the domain (perhaps all of it) — in which case it is called an absolute or global extremum (the latter term is common when the set is all of the domain).

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rdfs:label	Extreme value
rdfs:comment	An extreme value, or extremum (plural extrema), is the smallest (minimum) or largest (maximum) value of a function, either in an arbitrarily small neighborhood of a point in the function's domain — in which case it is called a relative or local extremum — or on a given set contained in the domain (perhaps all of it) — in which case it is called an absolute or global extremum (the latter term is common when the set is all of the domain).
dcterms:subject	Functions Differential calculus
abstract	An extreme value, or extremum (plural extrema), is the smallest (minimum) or largest (maximum) value of a function, either in an arbitrarily small neighborhood of a point in the function's domain — in which case it is called a relative or local extremum — or on a given set contained in the domain (perhaps all of it) — in which case it is called an absolute or global extremum (the latter term is common when the set is all of the domain). As a special case, an extremum that would otherwise be considered a relative/local extremum but occurs at an endpoint (or more generally a boundary) of the function's domain is sometimes called an endpoint or boundary extremum and is not considered a relative/local extremum, although it may be an absolute/global one. Note that in the case of relative/local extrema, it is common to concentrate on where the extrema occur (i.e., the "-values") rather than what the extreme values actually are (the "-values"), whereas in the case of absolute/global extrema it is common to concentrate on the extreme value itself (the "-value"). However, in either case both values may be given — e.g., if the extreme value 5 occurs at . Extrema can be found by taking the derivative of a function and setting it to equal zero. If the second derivative at this point is positive, it is a minimum, and vice versa..

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