在此基础上通过构造区间套依次证明了罗尔中值定理、拉格朗日中值定理和柯西中值定理。

On the basis of these theories, Rolle mean value theorem, Lagrange mean value theorem and Cauchy mean value theorem are proved by constructing nested interval.

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给出柯西中值定理的一个新的证法，说明柯西中值定理也可由拉格朗日中值定理导出。

This paper gives the new method to prove the cauchy mean value theorem which also may be deduced from the Lagrange mean value theorem.

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本文介绍了柯西中值定理的多种证明方法及其应用。

This paper introduces the proof and application of Cauchy mean-value theorem from many angles in every aspect.

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