Hopefully, by now you should have a good grasp on how (and when) to use the Lagrange multiplier method. The technique is used to find extrema on bounded surfaces that do not always work out nicely by simpler methods. Unfortunately, we cannot give you more useful examples (since Maple is being terribly unfroggy), but you should at least have a grasp on why the method works. If you still do not understand it, please talk to your professor or TA. We aren't trying to say that knowing how to use Lagrange multipliers is absolutely essential to getting a good grade in this class, but it is sure to make your homework a lot easier. May the Frog be with you! :)