Question: The function f(x,y) = 2xy has an absolute maximum value and absolute minimum value subject to the constraint 3x2 + 3y2-5xy= 121. Use Lagrange multipliers

The function f(x,y) = 2xy has an absolute maximum value and absolute minimum value subject to the constraint 3x2 + 3y2-5xy= 121. Use Lagrange multipliers to find these values. . . . Find the gradient of f(x,y) = 2xy. Vf (x,y) = ( 2y , 2x) Find the gradient of g(x,y) = 3x2 + 32 - 5xy - 121. Vg(x,y) = (6x - 5y , 6y - 5x) Write the Lagrange multiplier conditions. Choose the correct answer below. A. 2y = 2(6x - 5y), 2x = >(6y - 5x), 3x2+ 3y2-5xy - 121 =0 O B. 2xy = 1(6x - 5y), 2xy = 1(6y - 5x), 3x2+ 3y2-5xy - 121 = 0 O C. 2x =1(6x - 5y), 2y = 2(6y - 5x), 3x2 + 3y2-5xy - 121 = 0 O D. 2x = 1(6x - 5y), 2y = 1(6y - 5x), 2xy = 0

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