基于一阶偏导数判定多元函数极值的一个充分条件
A Sufficient Condition for Judging the Extreme Values of Multivariate Functions Based on the First-order Partial Derivative
涂淑珍 1马奕 1任雪芳1
作者信息
- 1. 龙岩学院数学与信息工程学院,福建龙岩 364000
- 折叠
摘要
在一元函数极值充分条件的基础上,用类比的方法给出二元函数极值的一阶充分条件,并推广到多元函数,且该充分条件适用于驻点和偏导数不存在点的判断,其证明过程只涉及到拉格朗日中值定理和偏导数的计算.
Abstract
This paper gives the first order sufficient conditions for extreme values of binary functions by an analogy to the sufficient conditions for the extreme values of the unary function,and extends the conclusions to the n-variate functions where n is greater than or equal to 3.The sufficient condition is applicable to the judgement of stationary point and the point where the partial derivative doesn't exist.The proof of the conclusion only involves the Lagrange Mean Value Theorem and first order partial derivative.It is more direct and concise than the current sufficient condition of the extreme values of the multivariate functions.
关键词
多元函数/极值/充分条件/偏导数/拉格朗日中值定理Key words
multivariate functions/extreme values/sufficient condition/partial derivative/the Lagrange Mean Value Theorem引用本文复制引用
基金项目
福建省教育科学规划课题(2020)(FJJKCG20-362)
龙岩学院教育教学改革研究项目(2023)(2023JY13)
出版年
2024
NETL
NSTL
万方数据