The function f(x,y) = 4xy has an absolute maximum value and absolute minimum value subject to the constraint 2x- + 2y- - 3xy = 49. Use Lagrange multipliers to find these values. Find the gradient of f(x,y) = 4xy. Vf(x.y) = (0 Find the gradient of g(x.y) = 2x2 + 2y2 - 3xy - 49. Vg(x.y) = (10 Write the Lagrange multiplier conditions. Choose the correct answer below. O A. 4x= 1(4x - 3y), 4y = M(4y - 3x), 2x2 + 2y2 - 3xy - 49=0 O B. 4y = 2(4x - 3y), 4x = M(4y - 3x), 2x2 + 2y2 - 3xy - 49=0 O C. 4xy = 1(4x - 3y), 4xy = M4y - 3x), 2x2 + 2y2 - 3xy - 49 =0 O D. 4x= 1(4x - 3y), 4y = M(4y - 3x), 4xy = 0 The absolute maximum value is The absolute minimum value is