Q4 (11 points) Use theorem 11.9 to show that the function 1/4 1/2 y =x defined on Ray is strictly 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; [ Hil > 0, [ H2| > 0. [H3| > 0. . ... [H.| = [H| > 0forx e R". In this case d'y > 0 and so f is strictly convex. 2. H is negative definite on IR" if and only if its leading principal minors alternate in sign beginning with a negative value for k = 1; [Hil 0. .... 1H.1 = 1HI zo > 0 if n is even if n is odd for x E IR". In this case d'y