optimization: maximize area of rectangle inside track
I have this problem i cannot figure out. It uses optimization:
There is a rectangular field with a semicircle on each end and a track around the whole thing. The perimeter of the inner edge of the track is 1256 meters.
I need to maximize the area of the rectangle. How do I do this?
You know the perimeter of the track:
The area of the rectangle is:
Solve  for x, sub into , differentiate, set to 0 and solve for r.