关于对称导数的中值定理及其逆问题  

Mean Value Theorem and Inversion of Symmetric Derivative

作　　者：李宏奕[1] 

机构地区：[1]广州广播电视大学侨光分校,广东广州510150

出　　处：《广州广播电视大学学报》2013年第1期103-106,112,共4页Journal of Guangzhou Open University

摘　　要：本文通过指出文献[1]中定理6和定理7的不合理性,重新给出对称导数下的Rolle定理、Lagrange中值定理、Cauchy中值定理和Taylor中值定理,并就Lagrange中值定理、Cauchy中值定理和Taylor中值定理的逆问题进行讨论证明。First, this paper illustrates the irrationality of Theorem 6 and Theorem 7 in Literature 1. Then the paper rede-fines Rolle Theorem, Lagrange's Mean Value Theorem, Cauchy's Mean Value Theorem, and Taylor's Mean Value Theorem of the Symmetric Derivative. Finally the paper discusses the inverse problem of Lagrange's Mean Value Theorem, Cauchy's Mean Value Theorem and Taylor's Mean Value Theorem.

关 键 词：对称导数 LAGRANGE中值定理 CAUCHY中值定理 TAYLOR中值定理 

分 类 号：O172.1[理学—数学]