1. The problem statement, all variables and given/known data I am trying to find the min and max values of f(x,y)=2x^2 + 3y^2 subject to xy=5. 2. Relevant equations f(x,y)=2x^2 + 3y^2 subject to xy=5 [itex]\mathbf\nabla[/itex]f=(4x, 6y) [itex]\mathbf\nabla[/itex]g=(y,x) 3. The attempt at a solution When I go through the calculations, I end up with two critical points, but both yield the same maximum value. Is this correct that there are two maxs and no min? I'm skeptical. Any suggestions are appreciated.