A variation of Cauchy's mean-value theorem (Q2708125)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A variation of Cauchy's mean-value theorem |
scientific article |
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16 May 2002
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Cauchy's mean-value theorem
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A variation of Cauchy's mean-value theorem (English)
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The following is called Flett's mean-value theorem: If \(f\) is differentiable on \([a,b]\) and NEWLINE\[NEWLINEf'(a)=f'(b)\tag{*}NEWLINE\]NEWLINE then there exists an \(x\in]a,b[\) such that \(\frac{f(x)-f(a)}{x-a}=f'(x)\) (in other words, a tangent can be drawn from the point \((a,f(a))\) to the \(]a,b[\) segment of the graph of \(f\)). Author offers a generalization where (*) is not required and the second derivative is also involved.
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