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。
Finally discusses the Lagrange mean value theorem proof method of constructing auxiliary function in order to expand on the idea of theorem proving.
最后探讨了拉格朗日中值定理证明中辅助函数的构造方法，以此拓展对定理证明的思路。
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。
The paper sums up the application of Lagrange mean theorem in five aspects in high mathematics, and give an example to illustrate its application.
总结了高等数学中拉格朗日中值定理五个方面的应用，并举例加以说明。
Finally, the condition and result of integral mean-value theorem are also improved combined with the Lagrange mean value theorem of differentials.
最后，结合拉格朗日微分中值定理改进了积分中值定理的条件和结论。
This paper deals with the forms of higher order of Cauchy′s mean value theorem, from which the author draws an inference of the forms of higher order of Lagrange′s mean value theorem.
本文论述柯西中值定理的高阶形式，并由此推出拉格朗日中值定理的高阶形式。
This paper deals with the forms of higher order of Cauchy′s mean value theorem, from which the author draws an inference of the forms of higher order of Lagrange′s mean value theorem.
本文论述柯西中值定理的高阶形式，并由此推出拉格朗日中值定理的高阶形式。
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