Q1 (10 points) Use theorem 11.9 to show that the function f (x1, x2) = x x2 , d 1/2 1/2, defined on R2, is concave. Theorem 11.9 Let H be the Hessian matrix associated with a twice continuously differentiable function y = f (x), x E R". It follows that: 1. H is positive definite on R" if and only if its leading principal minors are positive; [ Hi [ > 0. [ H2| > 0, [H3| > 0. . .. . [H,| = [H| > 0 for x E R". In this case d'y > 0 and so f is strictly convex. 2. H is negative definite on R" if and only if its leading principal minors alternate in sign beginning with a negative value for * = 1; [Hil 0. .... IHMI = 14| |>0 ifn is even for x E R". In this case day