Q1) i)[5 marks] Let S R 3 be a surface given by S = f 1(c) for f : R 3 R. Show that, for all p in S,f is perpendicular to the tangent space of S at p, TpS. ii)[5 marks] Let F : R 3 R be a smooth function. Suppose that the restriction of F to S has a local maximum or minimum at p in S, Show that pF is a multiple of pf.