Answer all questions in the booklets provided. Show your work: your grade will depend on the clarity and carefulness of your answer In addition to its correctness. You have 80 minutes. 1. 10 marks. Consider the function f(21, 12) = 2102 + 27. (a) 1 mark. Find the Gradient and Hessian of f. (b) 1 mark. What can you say about the curvature of f? (c) 2 marks. Find the first order total differential of f. (d) 3 marks. Consider the first-order Taylor series approximation to f around the point I1, 12 = (1, 1). Compute the error of this approximation at (1,0). (e) 3 marks. Consider the second-order Taylor series approximation to f around the point (1,1). Compute the error of this approximation at (1,0). Has it improved compared to the first-order approximation? 2. 10 marks. Consider the function Solve the problem max f(21, 12) subject to 0