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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:

Extremum	Description
local minimum	The least value of a function over a finite portion of the range of the function.
global minimum or absolute minimum	The least value of a function over its entire range.
local maximum	The greatest value of a function over a finite portion of the range of the function.
global maximum or absolute maximum	The greatest value of a function over its entire range.
Table 1: Type of extrema

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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.org. http://www.allmathwords.org/en/e/extremum.html.

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All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem.org and are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Revision History

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

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