6 2. (12 points) Use Lagrange multipliers to find the maximum values of the function f (x, y, z) = 2x + 2y + z subject to the constraint x2 + y2 + z2 = 9. V (x , y , z ) = 6 2, 2, 1 7 79 ( x,y, z ) = (2x, 24, 27 ) VI ( x, y, z ) = 1. Vg ( x, y, 2 ) ! = X2x (1) 2 = Ady (2 ) 1 = 122 (3 ) + 42 + 2 = 9 (4)3. (12 points) Let p(x, y) = 2 be the density function. Find the centroid (center of mass) of the lamina that occupies the region D enclosed by x = y' and x = 1.