关于微分中值定理逆的讨论

On Converse of Differential Mean Value Theorem

微分中值定理是说对于在每一点都可导的连续曲线的每一条弦都可以找到平行于该弦的切线,但对于每一条切线能否找到平行于该切线的弦呢?这一问题大多数教科书都很少涉及.该文就这一问题在什么条件下能实现进行了系统的论述,建立了微分中值定理的逆定理.对微分中值定理的教学有一定的参考与帮助作用.

Mean value theorem means that for each chord of the continuous curves derived from each point, a tangent can be found paralleling to this chord. But for each tangent, can a chord be found paralleling to this tangent？ Most of the textbooks deal little with this problem. This paper systematically discusses on what condition this is possible and establishes the converse theorem of differential mean value theorem, which is helpful for the teaching of differential mean value theorem.