maxima and minima

Also known as minima and maxima, variable's extreme values, extrema, extremum

largest and smallest value taken by a function in a given range

AI overview

Maxima and minima refer to the largest and smallest values that a function reaches within a given range. Understanding where these extreme values occur matters because it helps solve practical problems, from finding the best profit in a business to determining the safest design in engineering.

AI-generated from the Wikipedia summary — may contain errors.

~12 min read

Encyclopedic overview

Local and global maxima and minima for cos(3πx)/x, 0.1≤ x ≤1.1 Global and local extremums of a function.

In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extrema, 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. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.

Excerpted from Wikipedia’s “maxima and minima” article, available under the CC BY-SA 4.0 licence.