导函数的若干性质

The Characters of Derivatives

讨论导函数的若干性质:导函数具有介值性、导函数无第一类间断点。进而说明在区间Ⅰ上不具介值性或具 有第一类间断点的函数必定不存在原函数;具有第二类间断点的导函数可能存在原函数也可能不存在原函数。

The paper discussed the characters of derivatives that it has the character of intermediate value property and it has no the character of the discontinuity points of the first kind. Then it explained that the function in the Zone I without intermediate value property or with the discontinuity points of the first kind does not exist in the primitive functions; the derivatives with the discontinuity points of the second kind may exist in the primitive functions or may not exist in the primitive functions.