3. For each of the following, use Lagrange multipliers to find all extrema of f subject to the given constraints.

(a) f(x, y) = x + y2 and x2 + y2 = 4.

(b) f(x, y) = x2 - 4xy + 4y2 and x2 + y2 = l.

(c) f(x, y, z) = xy, x2 + y2 + Z2 = 1 and x + y + z = o.

(d) f(x,y,z,w) = 3x + y + w, 3x2 + y + 4z3 = 1 and -x3 + 3z4 + w = o.