曲线拐点充分条件证明中的常见错误  

The Common Errors in Proof of Sufficient Conditions of Judging Inflection Point

作　　者：陈玉[1] 

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022

出　　处：《大学数学》2010年第4期187-190,共4页College Mathematics

摘　　要：文[1]给出了判别曲线拐点的两个充分条件,文[2]给出了一个充分条件,但三个定理的证明都是错误的.同时,文[1]的两个推论也是错误的.本文通过反例分析了其错因,并给出了文[1]中一个拐点充分条件的正确证明.Two sufficient conditions in paper [1] and one sufficient condition in paper [2] are given to judge inflection point. But the proofs of them have mistakes and two corollaries in paper [1] are also wrong. This paper analyses the error reasons of them by some counter examples and gives a correct proof of one sufficient condition of paper [1].

关 键 词：拐点 导数 凹函数 凸函数 

分 类 号：O172.1[理学—数学]