# Extremum

Pronunciation: /ɪkˈstri.məm/ Explain

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

### References

1. McAdams, David E.. All Math Words Dictionary, extremum. 2nd Classroom edition 20150108-4799968. pg 77. Life is a Story Problem LLC. January 8, 2015. Buy the book

McAdams, David E. Extremum. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/e/extremum.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)