Question 1) Multivariate Calculus: (a) For the multivariate function f(x, y, z) = yr2 + zy2 - 22 - 2yx - 2zy + y - z (i) Find all the stationary points(s) of this function. (ii) Find the Hessian matrix. (ii) Classify only ONE of the stationary point(s) of your choice. (b) Find all values for k so that f(a, y) = 2 + kry + y' has a local minimum at (0, 0). Give your answer in the form of an interval. (c) Find the maximum and minimum values of f(x, y) =x2 + y- subject to xy = 16. [(6+6+6)+6+6= 30 marks]