一个幂函数不等式的推广  

Extension of an inequality with power function

作　　者：刘丹华 LIU Danhua(General Education Center,Zhengzhou Business University,Zhengzhou 451200,China)

机构地区：[1]郑州商学院通识教育中心,河南郑州451200

出　　处：《高师理科学刊》2023年第7期14-17,共4页Journal of Science of Teachers＇College and University

摘　　要：利用分类讨论和拉格朗日乘数法证明了高等数学课后习题中的一个三元幂函数不等式在指数一般化的情况下仍是成立的,补充了该不等式等号成立的条件.在此基础上,利用数学归纳法将该不等式由三元函数推广到n元函数.By using classification discussion and Lagrange multiplier method,it is proved that a three-variable power function inequality in after-school exercises of higher mathematics is still valid in the case of exponential generalization.The conditions for the equality of the inequality are supplemented.On this basis,the inequality is extended from three-variable function to-variable function by mathematical induction.

关 键 词：不等式 LAGRANGE乘数法 多元函数 

分 类 号：O178[理学—数学]