广义微分中值定理  

The generalized differential mean value theroem

作　　者：刘元会[1] 常安定[1] 邓秋霞[2] 

机构地区：[1]长安大学理学院,陕西西安710064 [2]武警工程学院通信工程系,陕西西安710086

出　　处：《纺织高校基础科学学报》2003年第4期294-297,共4页Basic Sciences Journal of Textile Universities

摘　　要：对于k阶可导函数,利用拉格朗日中值定理,证明了函数的k阶导数与函数值之间的关系;对于s阶可导函数(s>k),证明了函数的s-k阶导数值与函数的s阶导数之间的关系.给出了常见的k=2,k=3,k=4对应的定理及其证明.To the functions k-th derived,the relation between the values of the functions and the value of the k-th derived functions has been proved suing the lagrange mean value theorem. To the functions s-th derived (s>k) ,the relation between the values of the (s - k)-th derived functions and the value of the k-th derived functions has been given. To the situations k =2,3,4, according to the theorem above, the corresponding theorems have been given and proved.

关 键 词：高阶导数 中值定理 微分 

分 类 号：O172.1[理学—数学]