摘要
根据Cauchy微分中值定理表达式的结构引入辅助函数F(x,c)=f(x)-f(c)/g(x)-g(c)(a<c<b),通过讨论其可导性,得到相关的几个不等式,由此得出Cauchy微分中值定理存在唯一"中值点"的一个条件,并给出其逆定理的一个较弱表述.
Inspired by Cauchy's differential mean value theorem, we discuss the differentiability ofthe function F(x,c)=f(x)-f(c)/g(x)-g(c) (a〈c〈b), and obtain several inequalities related. Using theseinequalities, we obtain a sufficient condition for the uniqueness of the "mean value point" in Cauchy^s differential mean value theorem, and a weak form for its inverse theorem.
出处
《高等数学研究》
2013年第5期9-11,共3页
Studies in College Mathematics
关键词
CAUCHY微分中值定理
严格单调
左右导数
Cauchy's differential mean value theorem, strictly monotonicity, one side derivative