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.

Cite this article as:


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

Image Credits

Revision History


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

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License