Extreme value: Difference between revisions
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imported>Igor Grešovnik m (Created the article) |
imported>Igor Grešovnik m (notation) |
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The largest and the smallest element of a [[set]] are called '''extreme values'''. | The largest and the smallest element of a [[set]] are called '''extreme values'''. | ||
For a [[differentiable]] [[function (mathematics)|function]] ''f'', if ''f''(''x<sub>0</sub> | 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]]. | ||
Revision as of 22:49, 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.