考研数学试题的凸性理论拓展分析  

Extended Convexity Analysis of a Proof Problem in the Mathematics Postgraduate Entrance Examination

作　　者：张立国[1] 蔡春[2] ZHANG Liguo;CAI Chun(Department of Mathematics,Shenyang Ligong University,Shenyang 110159,China;Department of Mathematics and Science,Beijing Union University,Beijing 100191,China)

机构地区：[1]沈阳理工大学理学院,沈阳110159 [2]北京联合大学数理部,北京100191

出　　处：《高等数学研究》2022年第6期26-29,共4页Studies in College Mathematics

摘　　要：文中首先分析了2022年一道数学考研试题证明中二阶导数连续条件可以弱化,其次利用数形结合的思想方法,从几何的角度阐述了条件可以弱化的原因并给出弱化后的证明步骤,再次拓展函数凸凹性的结论.This paper analyzes a problem of the mathematics postgraduate entrance examination,and proves that the continuous condition of second derivative in the problem can be weakened.Using the method of combination of number and shape,we expound the reasons of weakened condition from the geometric perspective and provide our proof.

关 键 词：数形结合 凸凹性 连续 

分 类 号：O171[理学—数学]