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Mean value theorem (divided differences)
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Mean value theorem (divided differences) : ウィキペディア英語版
Mean value theorem (divided differences)
In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives.
==Statement of the theorem==

For any ''n'' + 1 pairwise distinct points ''x''0, ..., ''x''''n'' in the domain of an ''n''-times differentiable function ''f'' there exists an interior point
: \xi \in (\min\,\max\) \,
where the ''n''th derivative of ''f'' equals ''n'' ! times the ''n''th divided difference at these points:
: f() = \frac.
For ''n'' = 1, that is two function points, one obtains the simple mean value theorem.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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