﻿ Extremum: the least or greatest value of a function on a range.

# Extremum

Pronunciation: /ɪkˈstri məm/ ?

An extremum is a maximum or minimum value of a function. An extremum can be global - the maximum or minimum value on the entire range of a function, or local - the maximum or minimum value on an interval of a range. An extremum can be a finite number, positive infinity, or negative infinity. The types of extrema are:
ExtremumDescription
local minimumThe least value of a function over a finite portion of the range of the function.
global minimum or absolute minimumThe least value of a function over its entire range.
local maximumThe greatest value of a function over a finite portion of the range of the function.
global maximum or absolute maximumThe greatest value of a function over its entire range.
Table 1: Type of extrema

 Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Manipulative 1: Extrema. Click on the points on the purple sliders and drag them to change the figure.

Extremum. 2010-06-12. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/e/extremum.html.

### Revision History

2010-06-12: Combined articles on absolute maximum and absolute minimum. (McAdams, David.)

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