u(x, y) = 2ln(1 + 2) + 2ln(1+y) t+2 (a) [10 MARKS] Compute the Hessian matrix D²u(x, y). Is u concave or convex? (b) [4 MARKS] Give the formal definition of a convex set. (c) [8 MARKS] Using your conclusion to (a), show that I+(1) = {(z,y) € R² : u(x, y) ≥ 1} is a convex set. (d) [8 MARKS] Compute the 2nd order Taylor polynomial of u(x, y) at (0,0).