作者Eliphalet (真系废到冇朋友)
站内trans_math
标题Re: [多变] Lagrange
时间Mon Jun 18 17:38:39 2012
※ 引述《pig10381 (pig)》之铭言：
: In this case, find the stationary points for the function f(x,y) = x^2 - y^2,
: subject to constraint (x-4)^2 - y^2 = 1,Also identify the local minimum,maximum
: ,or neither of both.
: 我想请问一下，算出来极值点为 (5,0) 跟 (3,0)
: 为什麽 local minimum = 25,为(5,0)这点，local maximum = 9,为(3,0)这点
: 原因是为什麽？感谢
V(x,y) := f(x,y) - L*g(x,y), g(x,y):= (x-4)^2 - y^2 -1
=> stationary points
(4L/(1-L), 0) 代入限制式得 (5,0) 或 (3,0)
L = 5/9 L=3/7
L= 5/9 => D^2 V(5,0) = [8/9,0;0,0] 半正定 => local minimum
L=3/7 => D^2 V(3,0) = [-8/3,0;0,0] 半负定 => local maximum
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