Problem 1 (11 points) For every part of this problem, let F(z, y, 2) = x + y + 2 - 28. (a) (1 pt) Compute the gradient VF. (b) (1 pt) Find a vector normal to the surface F(r, y, z) = 0 at the point P = (3, 7, 1). (c) (2 pts) Let z be defined implicitly by the equation F(r, y, z) = 0. Using implicit differen- tiation, compute s and #, at the point P = (3, 7, 1). Problem 1, continued (d) (7 pts) As before, let F(x, y, z) = r + y + 2 -28. Now, in addition suppose r(s, t) = (3s, st, t) and h(s, t) = F(r(s,t)). (i) Compute gh. (ii) Compute an (iii) Compute the the directional derivative of h(s, t) at the point (s, t) = (1, -5) in the direction of v = (1, 1)