# 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** (PL: **maxima** or **maximums**) and **minimum** (PL: **minima** or **minimums**) of a function, known generically as **extremum** (PL: **extrema**), are the largest and smallest value of the function, either within a given range (the *local* or *relative* extrema), or on the entire domain (the *global* or *absolute* extrema).[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.