※ 引述《pig10381 (pig)》之銘言：
: 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.
: 我想請問一下，算出來極值點為 (5,0) 跟 (3,0)
: 為什麼 local minimum = 25,為(5,0)這點，local maximum = 9,為(3,0)這點
: 原因是為什麼？感謝
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] 半負定 => local maximum
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