摘要
求解条件极值的基本方法为拉格朗日乘数法,直接从隐函数组出发推导拉格朗日乘数法既繁琐又不易让人理解,但注意到在一定的条件下,二元函数[f(x,y)]的极值点必定出现在该函数的等高线与约束曲线[g(x,y)=0]的切点上,由于等高线和约束曲线上任意一点处的梯度向量[▽,▽g]分别垂直于该等高线和约束曲线,可以得到[▽,▽g]在极值点处相互平行的几何结论,从而容易得出拉格朗日乘数法。
Lagrange multipliers is the basic method to solve the problem of conditional extremum in actual teaching. Deriving Lagrange multipliers directly from the group of implicit function is not only cumbersome but also difficult to understand. It should, however, be noted that in certain conditions, the extreme points of binary function [f(x,y)] will appear in the points of tangency between the contours of the curve and constraint curve [g(x,y)=0], since the gradient vector of the contour curve[▽f,▽g] is perpendicular to this contour curve itself, so does the constraint curve. We can get the geometric conclusion that the[▽f] and [▽g] are parallel to each other at extreme points, so Lagrange multipliers is very easy to get. In this paper, we use the powerful mapping functions of MATLAB to reproduce the vivid image of this process so as to help the students understand the geometry and mathematical thinking of Lagrange multipliers.
作者
唐家德
TANG Jiade(School of Mathematics & Statistics, Chuxiong Normal University, Chuxiong, Yunnan Province 675000)
出处
《楚雄师范学院学报》
2019年第3期10-15,共6页
Journal of Chuxiong Normal University
