Extreme value: Difference between revisions
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For a [[differentiable]] [[function (mathematics)|function]] ''f'', if ''f''(''x''<sub>0</sub>) is an extreme value for the set of all values ''f''(''x''), and if ''f''(''x''<sub>0</sub>) is in the [[interior]] of the [[domain (mathematics)|domain]] of ''f'', then ''x''<sub>0</sub> is a [[Critical_point_(mathematics)|critical point]]. | For a [[differentiable]] [[function (mathematics)|function]] ''f'', if ''f''(''x''<sub>0</sub>) is an extreme value for the set of all values ''f''(''x''), and if ''f''(''x''<sub>0</sub>) is in the [[interior]] of the [[domain (mathematics)|domain]] of ''f'', then ''x''<sub>0</sub> is a [[Critical_point_(mathematics)|critical point]]. | ||
== See also == | |||
*[[Maxima and minima]] | |||
Revision as of 22:52, 23 November 2007
The largest and the smallest element of a set are called extreme values.
For a differentiable function f, if f(x0) is an extreme value for the set of all values f(x), and if f(x0) is in the interior of the domain of f, then x0 is a critical point.