Stuck at d) and e)

3. Let g(x, y) = 1/2 k^2 (x + 1)^2 + k cos y xy.

(a) Calculate the gradient vector g(x, y).

(b) Calculate the Hessian matrix Hg(x, y).

(c) Find the second order Taylor polynomial of g at (0, ). Give your final answer as a polynomial, without using matrices or vectors.

(d) For what value(s) of k is (0, ) a critical point of g?

(e) For each of the k values in part (b), classify (0, ) as a local maximum, local minimum or saddle point.