(a) Find all critical points of the function f(x, y) = x 3 + 3y − y 3 − 3x and classify them as local minima, local maxima or saddle points. [10 marks] (b) For each critical point (x0, y0) you have identified in part (a) above, calculate the Taylor series expansion of f(x0 + δx, y0 + δy) about the point (x0, y0) up to (and including) quadratic terms. By considering in each case the sign of f(x0 + δx, y0 + δy) − f(x0, y0) for all δx and δy of sufficient small magnitude justify your conclusions in part (a)