Minima and maxima

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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).



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 |xx*| < 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 ≤.

See also