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.

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。

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

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。

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Secondly, the Lagrange mean value theorem in some proof of identity and the inequality in a wide range of applications.

其次，拉格朗日中值定理在一些等式和不等式的证明中应用十分广泛。

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