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

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

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