1. The problem statement, all variables and given/known data A rectangle has sides on the x and y axes and a corner on the plane x+3y=12. Find its maximum area. 2. Relevant equations A=xy=(12-3y)y (A=12, according to the solution manual.) 3. The attempt at a solution At first I thought the corner it was talking about lay on one of the axes, but now I realize that it is a point around (4,3). I know there is a derivative (partial?) I need to take, but I don't know which one and or what to do it with respect to. I've drawn a graph so I can see what I'm doing, but the professor just skimmed over maximixation and I'm really confused! This chapter is not at a point that Lagrange multipliers have been covered. That's the way I would expect to do it, obviously not.