PLEASE HELP ME SOLVE THESE QUESTIONS! THANKS!

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: 3 122 - 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. 4. Classify the stationary points of the following two functions: (a) m : R3 - R m (ac) = a Ax + b, (4) where: 3 -1 A = -1 3 (5) 1 -3 and b = 2. Is m (x) a quadratic form? (b) p: R2 _> R defined by: p(a) = xle 21(x2 - 42). (6) Are any of the stationary points of p(x) global extrema? Why/why not