n元函数微分中值定理探究

A Study of the Differential Mean Value Theorem to the Function of n-variables

利用方向导数,推导了n元函数的微分中值定理,并通过一定的分析,从形式和内蕴上探究了它与一元函数的微分中值定理的统一性,从而由直观和本质上对n元函数的微分中值定理有了全新的认知和更深刻的理解.

By using the directional derivative,we prove the differential mean value theorem to the function of n-variables,including Fermat′s lemma,Rolle′s theorem,Lagrange′s mean value theorem and Cauchy′s mean value theorem.We analyze the form and intrinsic unity of the differential mean value theorem to the function of one variable and the function of n-variables.Thus,for the differential mean value theorem to the function of n-variables,we have a brand-new cognition and deeper understanding.