3 . Perform the indicated computation. (a) (5 points) Compute fzzz for f(3:, y, z) = 332yz2 + ze2m (b) (5 points) Compute the maximum rate of change of the function f (3:, y, z) = xyz 3:23; at the point (1, 1, 0) and indicate the unit vector in the direction which this occurs. (92 . . . . (c) (10 points) Compute Z where 3:3 + y3 + Z3 + 633w: = 1 is assumed to implicitly dene . 63:2 2 as a function of :1: and y. . (20 points) Suppose u = u(a:, y) and v = v(a:, y) are differentiable and satisfy a_u _ 61} au Q 6:1: 6y 6y 8:5 If a: = rcost9 and y = rsin6 prove that Bu _ 1 31) av _ 1 an armanda'm . (10 points) Find and classify all the critical points of the function f (3:, y) = 3:2 333; + y3 y. . (20 points) Find the maximum and minimum values of f (:13, y, z) = :1: y + 22 on the sphere +f+=8 . (20 points) Find the point (:13, y) in R2 that has the largest possible yvalue and lies on the curve in R2 dened by the equation y2 = a: + 22323