"A 10-meter length of wire is available for making a circle and a square. How should the wire be distributed between the two shapes to maximize the sum of the enclosed areas?"
Here's what I have: $$Area_c = \pi r^2$$ $$Area_s = 4r^2$$
So, I'm thinking that I need to find the maximized radius size to figure everything else out. $$Area_c + Area_s = 10$$ $$(\pi r^2) + (4r^2) = 10$$
$${\operatorname{d}\over\operatorname{d}r} [(\pi r^2) + (4r^2) - 10] = 2\pi r + 8r$$
But here's my dilemma; if I take the derivative of that and solve for $r$, it comes out 0. So I'm not sure where I'm going wrong. Any advice?