5. This question gives you some practice with a type of preference called "Cobb- Douglas preferences" which shows up in many applied economic models because they are easy to do calculus with.] Let X = R2 , let u : X - R be given by u(x) := xx?, and let ~ be the preference relation on X given by utility representation u. Show that: (a) The function u is not concave. [Hint: Take a second partial derivative with respect to one of the coordinates.] (b) The preference relation ~ is convex. Hint: You may use the fact that the function f : X - R given by f(x) = 21 22- 1/2x1/2 is concave. If you feel like doing some math, try to show that f is concave, but you don't need to do this