【摘要】 本文是将微分学三个重要定理(洛尔、拉格朗日、柯西定理)中的函数在开区间上可微的条件放宽为函数在开区间上每一点左、右导数均存在的条件,得到了相应的包含了原三个定理情况的三个定理,它们是微分中值定理的推广。同时,给出了三个推广定理的证明,并举例说明。从而得出三个推广定理是完全正确的。更多还原

【Abstract】 In this paper,the conditions required by three important theorems in differential calculus(Rolle Theorem, Lagrange Theorem and Cauchy Theorem) -the function have to be defferentiable on open interval,are modified to the conditions that the function has left derivative and right derivative at every point on the open interval,and the new theorems generalizing the original ones are obtained. These are the extended differential median theorems. Besides, three extended theorems are proved and some examples are illustrated. The conclusion is: three extended theorems are completely true.更多还原