Maximum and minimum of a function

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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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098