拉格朗日中值定理逆命题成立的一个充要条件

A Necessary and Sufficient Condition for the Converse of Lagrange’s Mean Value Theorem

本文针对《高等数学》拉格朗日中值定理逆命题成立的条件进行研究,采用函数曲线与割线的位置关系证明了文献[3,4]给出的充分条件,同时本文还给出并证明了拉格朗日中值定理逆命题成立的一个充要条件,以及判别方法.

This paper studies conditions for the converse of Lagrange’s mean value theorem. We verify the sufficient condition given in [3, 4] based on the positional relationship between the curve of a function and its secant. We prove also a necessary and sufficient condition for the converse of Lagrange’s mean value theorem along with a criterion.