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\f(5) Consider the function f(x,y) = xy- x -y (a) Determine the extreme points of f in the set R?. 5 points (b) Classify the extreme points of f in the set R' and justify if they are local or global extreme points. 5 points(4) Consider the set of equations ry + zy cty-2 0 (a) Prove that the above system of equations determines implicitly two differentiable functions y(r) and =(x) in a neighborhood of the point (x, y. =) = (0, 1, 1). 4 points (b) Compute y/'(0), ='(0) and the first order Taylor polynomial of y(x) and =(x) at the point ro = 0. 6 points(3) Consider the function f(z, y) = ard + ay' - 2ry where a E R is a parameter and a > 0. (a) Compute the gradient and the Hessian matrix of the function f. Compute the Taylor polynomial of degree 2 of f, centered at the point r = 0, y = 1. Compute the critical points of f. 5 points (b) Determine the largest open set of R- where the function f is concave or convex, depending on the values of the parameter a. 5 points(2) Consider the set A = {(r, y) ER' : 0