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Lagrange multiplier to find the point?

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  • Lagrange multiplier to find the point?


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Answer #1 | 14/01 2014 09:29
Minimize (x-1)^2 + y^2 + (x+1)^2 + y^2 subject to 2x+3y-4=0. f(x,y) = (x-1)^2 + y^2 + (x+1)^2 + y^2 + λ (2x+3y-4) f(x,y) = (x-1)^2 + (x+1)^2 + 2 y^2 + λ (2x+3y-4) ∂f/∂x = 2(x-1)+2(x+1)+2 λ = 0 4x+ 2 λ = 0 λ= -2x ∂f/∂y = 4y+ 3 λ = 0 λ= (-4/3) y -2x = (-4/3) y x = (2/3) y y = (3/2) x 2x+3y-4 =0 2x+ 3(3/2)x - 4 = 0 2x+(9/2) x - 4 = 0 x=8/13 y = (3/2)(8/13) = 12/13 (x,y) = (8/13, 12/13) It will be at (8/13, 12/13) when the sum of the squares of its distances from (1, 0) and (-1, 0) is smallest.
Positive: 75 %

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