The circumference is equal to 10, I am to find x and y (as drawn on the picture) so that the area is as great as possible. I have tried back and forth here.
$A = \frac{\pi y^2}{8} +xy$
$10 = \frac{y\pi}{2} + 2y + 2x $
When finding a maximum I know derivation is the way to go, but here there is two variables. And this is an introductory course, and derivation with multiple variables is not a part of curriculum. I tried to solve the circumference function for x and y, and then substituting the values into the function for the area. And then finding the derivative for each function separately, but that didn't work. Well, it worked but the book doesn't agree on the answer.