# Maximum and minimum of a function

From Encyclopedia of Mathematics

A largest, respectively smallest, value of a real-valued function. A point of the domain of definition of a real-valued function at which a maximum or minimum is attained is called a maximum or minimum point, respectively (see Maximum and minimum points). If some point is an absolute (local) maximum or minimum point, strict or non-strict, then the value of the function at that point is correspondingly called an absolute (local), strict or non-strict, maximum or minimum. A continuous function on a compact set always takes maximum and minimum values on that set.

All together, the maxima and minima of a function are called its extrema or extremal values.

**How to Cite This Entry:**

Maximum and minimum of a function. L.D. Kudryavtsev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Maximum_and_minimum_of_a_function&oldid=16316

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098