Re: [考古] 96東華
※ 引述《pp20624 (kk)》之銘言：
: Find the extreme values of
: f(x,y)=x^2 +2y^2 -2x + 3
: subject to the constraint x^2+y^2≦10
: 我算到
: f(t)=10sin^2 t -2√10 cost+13 就卡住了
: 也不知道對不對
: 有請先進指點 感謝您
我是用Lagrange
L(x,y,z) = x^2 + 2y^2 - 2x + 3 +λ(x^2 + y^2 - 10)
Lx = 0
Ly = 0 => (x,y) = (√10,0) (-√10,0) (-1,3) (-1,-3)
Lλ = 0
because the constraint x^2+y^2≦10
fx = 0
fy = 0 => (x,y) = (1,0)
so, max value = 24 , min value = 2
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