5. Evaluating [quasi-]concavity a) Show that f (x,z) = x1/2z1/4 is both concave and quasi-concave. Assume x > 0 and z > 0. b) Show that f(x,z) = x5/2z5/4 is quasi-concave but not concave. Assume x > 0 and z > 0. c) Show that the second-order conditions for obtaining a maximum will always be satisfied in the case of a consumer who maximizes a strictly quasi-concave utility function subject to a linear budget constraint. You can assume that utility is only a function of two goods