Use theorem 11.6 to show that the function f(x1,x2)=x11/2x21/3 defined on R++2, is concave. Let H be the Hessian matrix associated with a twice continuously differentiable function y=f(x),xRn. It follows that: 1. H is positive definite on Rn iff its leading principal minors are positive; H1>0,H2>0,H3>0,, Hn=H>0 for xRn. In this case, f is strictly convex. 2. H is negative definite on Rn iff its leading principal minors alternate in sign, beginning with a negative value for k=1 : Use theorem 11.6 to show that the function f(x1,x2)=x11/2x21/3 defined on R++2, is concave. Let H be the Hessian matrix associated with a twice continuously differentiable function y=f(x),xRn. It follows that: 1. H is positive definite on Rn iff its leading principal minors are positive; H1>0,H2>0,H3>0,, Hn=H>0 for xRn. In this case, f is strictly convex. 2. H is negative definite on Rn iff its leading principal minors alternate in sign, beginning with a negative value for k=1