# Maximum and minimum

## Largest and smallest value taken by a function takes at a given point / From Wikipedia, the free encyclopedia

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In mathematical analysis, the **maximum** and **minimum**^{[lower-alpha 1]} of a function are, respectively, the largest and smallest value taken by the function. Known generically as **extremum**,^{[lower-alpha 2]} they may be defined either within a given range (the *local* or *relative* extrema) or on the entire domain (the *global* or *absolute* extrema) of a function.^{[1]}^{[2]}^{[3]} 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.

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