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A maximum or minimum value of a real-valued function. (Cf. Maximum and minimum points.) In the calculus of variations the term "extremum" is also used in the study of greatest or smallest values of a functional.


Cf. also Maximum and minimum of a function.

In variational calculus the term extremal for a curve on which a function(al) attains its maximum (or minimum) values is often used.

How to Cite This Entry:
Extremum. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098