方向导数与二元函数极值的充分条件  

Directional Derivative and the Sufficient Condition of the Extreme Value for Two-variable Function

作　　者：杨金花[1] 田冲[2] 

机构地区：[1]河南理工大学,河南焦作454000 [2]周口师范学院,河南周口466000

出　　处：《平顶山学院学报》2011年第5期11-14,20,共5页Journal of Pingdingshan University

摘　　要：分别给出了P0(x0,y0)的l0珒正方向δ邻域和l0珒负方向δ邻域的定义,用方向导数表示了二元函数的泰勒公式,使之与一元函数的泰勒公式有统一的形式;并利用二元函数泰勒公式的方向导数形式给出了二元函数取得极值的3个充分条件,使之与一元函数取得极值的3个充分条件相对应.In this paper,the definition of positive direction neighborhood of a point P0（x0,y0） and its negative direction neighborhood are given.Taylor＇s formula of two-variable function is given by the use of directional derivative,which is in accord with Taylor＇s formula of one-variable function.Meanwhile,three sufficient conditions of two-variable function extreme value are given with directional derivative of Taylor＇s formula of two-variable function,which are in accord with one-variable function.

关 键 词：方向导数 极值 二元函数 泰勒公式 

分 类 号：O174[理学—数学]