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extended mean-value theorem
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(Theorem)
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Let $f:[a,b]\to\mathbb{R}$ and $g:[a,b]\to\mathbb{R}$ be continuous on $[a,b]$ and differentiable on $(a,b)$ Then there exists some number $\xi\in(a,b)$ satisfying: $$(f(b)-f(a))g^\prime(\xi)=(g(b)-g(a))f^\prime(\xi).$$ If $g$ is linear this becomes the usual mean-value theorem.
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"extended mean-value theorem" is owned by mathwizard.
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See Also: mean-value theorem
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Cauchy's mean value theorem, extended mean value theorem, generalized mean value theorem |
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Cross-references: mean-value theorem, number, differentiable, continuous
There are 2 references to this entry.
This is version 6 of extended mean-value theorem, born on 2002-09-28, modified 2003-10-23.
Object id is 3478, canonical name is ExtendedMeanValueTheorem.
Accessed 11838 times total.
Classification:
| AMS MSC: | 26A06 (Real functions :: Functions of one variable :: One-variable calculus) |
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Pending Errata and Addenda
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