PLEASE HELP ME SOLVE THIS QUESTION! THANK YOU!

3. (a) Let k : X C R" - R be a function defined on the finite set X = {X1, X2, ....., In) . Argue that k achieves a minimum and a maximum on X. Is this a consequence of the Weierstrass theorem? (b) Use the implicit function theorem to show that the equation: one"12 - 2x1 + 3x2 -4=0 defines x2 as a function of x1 in an interval around the point x = (0, 1). Find the derivative of this function at x1 = 0