多元函数条件极值的求法探究  

Discussions about Calculation of Conditional Extreme of Multivariate Function

作　　者：方倩珊[1] 吴全荣[1] 

机构地区：[1]漳州城市职业学院教师教育系,福建漳州363000

出　　处：《福建师大福清分校学报》2014年第2期5-10,共6页Journal of Fuqing Branch of Fujian Normal University

摘　　要：结合具体实例,分别从代入消元法、拉格朗日乘数法、几何模型法、参数方程法、梯度内积法、不等式法等六个角度探讨了多元函数条件极值的多种求法,比较了各种求法适用的条件,并指出某些教材中多元函数条件极值求法的不严谨性。旨在帮助学生在求解此类问题时选择适当的方法,把握正确的解题方向。Combined with examples, this paper first discussed six methods about calculation of conditional extreme of multivariate function： the substitution elimination method, the Lagrange multiplier method, the geometrical model method, the parametric equation method, the gradient inner product method, inequality method. And then it analyzed applicable condition of various calculation methods and pointed out the non-precise aspects in some textbooks about calculation of conditional extreme of multivariate function in order to help students choose the appropriate method when solving such problems.

关 键 词：多元函数 条件极值 稳定点 

分 类 号：O174.1[理学—数学]