导函数的特殊性质

The Special Properties of the Derivative Functions

文章讨论了导数的连续性 ,得到了导函数有极限必连续以及导数值存在时导函数间断必振荡等结论。文章研究了导函数的介值性 ,发现介值性不需要有连续的前提 ,同时指出了导函数振荡间断回归性的更深刻内涵。

In this paper,we have discussed the continuityof the derivative function,and obtained the conclusions that the derivative function must be continuous if its limit existed on a point and the discontinuous point of the derivative function must be the point of oscillatory discontinuity if the derivative existed and so on.We also have studied the intermediate value property of the derivative function,and found this property is not dependent on the continuity,meanwhile,we point out some more profound intension of the regression property of the oscillation-type gap of the derivative function.