Question 4) Now, let's solve some optimisation problems. (a) Linearise the function f(x, y) = V2 + 3y - at the point (3, 1). (b) Find the second order Taylor polynomial for f(x, y) = e'" In(1 + y) at the point (0, 0). (c) For the multivariate function f(x, y, z) = yx +zy' + =2 - 2yx + 2zyty - z (i) Find all the stationary points(s) of this function. (ii) Find the Hessian matrix. (ii) Classify the stationary point(s). (d) Find all values for k so that f(x, y) = 2 + key + y' has a local minimum at (1, 1). Give your answer in the form of an interval. (e) Find the maximum and minimum values of f(x, y, =) = -x - y + = subject to r' + y" = 2 and a ty += =1