The function f(x,y,z) = 8x - 4y + z has an absolute maximum value and absolute minimum value subject to the constraint x2+ y2 + z? =81. Use Lagrange multipliers to find these values. Find the gradient of f(x,y,z) = 8x - 4y + z. Vf(x,y,z) = 0 Find the gradient of g(x,y.z) =x2+ y2 +z2 -81. Vg(x.y.z) = 000 Write the Lagrange multiplier conditions. Choose the correct answer below. O A. 8=1(2), -4=1(2), 1=2(2), x2+ 12+22-81=0 O B. 8=12x), - 4=12y), 1 = M2z), 8x - 4y +z=0 O c. 8=12), -4=12), 1=12), 8x - 4y +2=0 O D. 8=1(2x), - 4=1(2y), 1= 12z), x2+ 12+22-81=0 The absolute maximum value is The absolute minimum value is