一类中值定理双介值问题命题的注记  

Notes on Setting Double-Parameter Quesdtions Related toMean Value Theorems for Derivatives

作　　者：龚致宾 楼红卫[1] GONG Zhi-bin;LOU Hong-wei(School of Mathematical Sciences, Fudan University, Shanghai 200433, China)

机构地区：[1]复旦大学数学科学学院,上海200433

出　　处：《大学数学》2021年第5期120-124,共5页College Mathematics

摘　　要：在中值定理类双介值问题的命题中,很多命题者没有注意到结论的平凡性.文章借助于微分Darboux定理,证明了对应的非平凡问题解的存在性.In constructing examples of double-parameter quesdtions related to mean value theorems for derivatives,many authors did not notice the triviality of the examples.This paper points out the triviality of many examples of this kind.Moreover,by using Darboux’s theorem for differentiable funcdtions,it is proved that nontrivial soludtions in fact exist.

关 键 词：中值定理 双介值问题 微分Darboux定理 

分 类 号：O172[理学—数学]