单侧导数和对称导数混合方式下的微分中值定理

Differential Mean Value Theorem Generalized with the Mixed Methods of One-sided Derivative and Symmetric Derivative

微分中值定理是分析中的一个重要定理,文[1-2]用对称导数讨论该定理,文[3-4]用单侧导数讨论该定理,而本文把两种导数结合起来以混合方式给出该定理的三种形式,且条件更弱.

The differential mean value theorem is an important theorem in analysis . The theorem is discussed with symmetric derivative in paper [1-2] ,and with one-sided derivative in paper [3-4]. But in this paper, three forms of the theorem is given with the mixed methods of one-sided derivative and symmetric derivative, and its conditions are weaker.