T Let f(x) = f(x, x2) = x ln(x + 1), where x S = {[x, x2] : x R, x2 0}. X1 X2 (a) Is the set S open or closed or both or neither? Is S bounded or unbounded? Is S convex or non-convex? What is the interior of S? (Note: No steps are required for (a).) (b) Determine the gradient vector Vf(x) and the Hessian matrix V2 f(x) over S. (c) Find V2 f(x, 1), for all x R. Let v = [v, v] be a non-zero column vector. Calculate vT V2 f(x, 1) v. Hence, or otherwise, show that V f(x,1) is indefinite by definition.