Minima and maxima: Difference between revisions
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imported>Igor Grešovnik (→Minimum: maximum - definition) |
imported>Jitse Niesen m (spelling) |
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In [[mathematics]], '''minima''' and '''maxima''', known collectively as '''extrema''', are the | In [[mathematics]], '''minima''' and '''maxima''', known collectively as '''extrema''', are the ''smallest value'' (minimum) or ''largest value'' (maximum), that a [[function (mathematics)|function]] takes in a point either within a given neighbourhood (local extremum) or on the whole function [[domain (mathematics)|domain]] (global extremum). | ||
== Definition == | == Definition == | ||
Revision as of 10:38, 18 January 2008
In mathematics, minima and maxima, known collectively as extrema, are the smallest value (minimum) or largest value (maximum), that a function takes in a point either within a given neighbourhood (local extremum) or on the whole function domain (global extremum).
Definition
Minimum
A real-valued function f is said to have a local minimum at the point x*, if there exists some ε > 0, such that f(x*) ≤ f(x) whenever |x − x*| < ε. The value of the function at this point is called minimum of the function.
The definition of a local maximum is similar, only with the ≥ sign in place of ≤.