1. The problem statement, all variables and given/known data f(x,y) = X[tex]\alpha[/tex]Y[tex]\beta[/tex] (that's X to the power of alpha, Y to the power of Beta) Is this function convex? Prove it. 2. Relevant equations f''(x,y) > 0 ==>convexity 3. The attempt at a solution My steps are as follows: f(X,Y) = (X^a)(Y^ß) f’(X,Y) = (aX^a-1)(Yb) + (X^a)(bY^b-1) f’’(X,Y) = ((a^(2)-a)X^a-2)(Yb) + (aX^a-1)(bY^b-1) + (aX^a-1)(bY^b-1) + (X^a)((b^(2)-b)Y^b-2) I'm just trying to simplify it to prove it is greater than 0 (or not). Is my work correct so far and how can I be sure the second derivative is indeed positive? Thanks a lot.