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1·In this paper, the Rolle's theorem of a variadle function is extended to multiple-variable functions. The paper, then, gives a new and simple proof.

本文将一元函数的罗尔定理推广到多元函数中，并给出了一个简洁、颖的证明。

2·Rolle's theorem plays a very important part in the study of one differential calculus. This paper attempts to explore the application of Rolle's theorem from the perspective of constructing function.

罗尔定理在一元微分学处于很重要的地位，本文通过构造函数的思想来探究罗尔定理的应用。

3·Cauchy's theorem of the mean is proved by means of nested intervals, with Rolle's and Lagrange's theorems of the mean as its corollaries.

本文根据区间套的方法，证明柯西中值定理，而把罗尔定理和拉格朗日中值定理作为它的推论。