Can someone show I how to find the min? I found the max =80/3 but don't know is it correct or not.  Thank all who been answer my questions.?

Find the maximum and minimum values of the function f(x,y)=4x^2 +9y^2 subject to xy = 4. Use Lagrange multipliers.

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  • Vaman
    Lv 7
    4 weeks ago
    Favourite answer

    Use L=Lagrange multiplier. Define a function g(x,y)= f(x,y) -L(xy-4)

    Take partial derivative of g wrt x and y to find L value. Take partial derivative wrt x and equate that to 0. You have 8x-Ly=0, When you do wrt y, you get 18y-Lx=0.  When solved, you have

    8x^2-18y^2=0, 4x^2-9y^2=0, 2x=+/-3y. xy=4, Select the positive value. 3/2y^2=4. y=sqrt(8/3), x=4/y=+/-4sqrt (3/8). For x positive value f(x,y)=4*16*3/8-9*8/3=24-24=0. This is the minimum value.

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