# Math Help - Confusing problem

1. ## Confusing problem

Well I've been working on this extra-credit problem for a looong time; but I'm not not sure if I'm doing it right when I attempt to solve it. It's really confusing me for some reason and frankly I just don't feel like I know what I'm doing when I'm trying to work it out. So, if someone doesn't mind, I'd really appreciate just seeing how I'm supposed to do this; I don't think I have a very good grip on these yet..Here's the problem:

2. The question asks for the height of the lamp above the table, so it would be a good idea to start by saying "Let h be the height of the lamp above the table."

Then you should find expressions for $l$ and $\cos\phi$ in terms of h, and put those into the formula for I. Then differentiate to find the value of h that maximises I.