The content of intermediate value theorem of the derivative is given and strictly proved by using various methods.
给出了导数的介值定理的内容，并用不同的方法对定理进行了严格的证明。
We proved the intermediate value theorem for continuous function at closed interval by constructing auxiliary sequence ingeniously and applying compact theorem as well as Cauchy convergence criterion.
通过巧妙地构造辅助数列，应用致密性定理、柯西收敛准则来证明闭区间上连续函数的介值性定理。
This paper points out and revises some errors in the results found in four articles concerning the asymptotic behavior of the "Intermediate points" of the mean value theorem.
本文指出了有关微分中值定理“中间点”的渐近性四篇文章的结果中的错误，并给予修正。
This paper is devoted to studying the asymptotic behavior of the intermediate point in the mean value theorem for first form curve integrals. A general result is obtained.
讨论了第一类曲线积分中值定理“中间点”的渐近性质，得到了更具一般性的新结果。
The continuity and derivative of the intermediate point in the Taylor mean value theorem are discussed, and some of their sufficient conditions are presented.
讨论泰勒中值定理中中值点的连续性及可导性问题，给出泰勒中值定理中中值点连续及可导的充分条件，同时给出计算其导数的公式。
By increasing the condition of the integral mean value theorem, we prove that the existence of intermediate point and the existence of interval are corresponding to each other.
给出了积分中值定理的一个注记，证明了中值点的存在性与覆盖中值点的区间的存在性是相互对应的。
The continuity and derivative of the intermediate point in the Taylor mean value theorem are discussed, and some of their sufficient conditions are presented.
讨论了积分中值定理中间点的单调性、连续性、可导性，给出了一组充分条件，并证明了三个相关定理。
The continuity and derivative of the intermediate point in the Taylor mean value theorem are discussed, and some of their sufficient conditions are presented.
讨论了积分中值定理中间点的单调性、连续性、可导性，给出了一组充分条件，并证明了三个相关定理。
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