1. The problem statement, all variables and given/known data Seems straightforward enough, Lagrangian optimization 2. Relevant equations Find the max of x^-1 + y^-1 subject to the constraint m=x+y 3. The attempt at a solution At first I thought no problems, x*=y*=m/2, however: Using the Lagrangian formula yields derivatives as follows: wrt x: -x^-2 - lambda wrt y: -y^-2 - lambda lambda: m-x-y Putting the coefficients into a bordered Hessian seems to give a positive def. matrix implying a minimum? Is this a trick question or is it possible to maximize?