基于曲线导数的二元函数微分中值定理

Differential Mean Value Theorems Based on the Curve Derivative of Binary Function

给定二元函数,文献[1]定义了其在光滑曲线上的方向导数(简称为曲线导数).本文主要利用曲线导数建立二元函数的微分中值定理,比如罗尔定理,拉格朗日中值定理,柯西中值定理.这些中值定理可视作一元函数微分中值定理在二维情形的推广.

For a given binary function, its＇ directional derivative on a smooth curve is defined in referenceEll （often called curve derivative briefly）. Some differential mean value theorems of binary function are studied based on The Curve Derivative, such as Rolle theorem, Lagrange mean value theorem and Cauchy mean value theorem. These differential mean value theorems can be viewed as a generalization of the one of one variable function.