posted by Tezuka .
A rectangle is bounded by the x-axis and the semicircle y=ã(25-x^2).
Question is, what length and width should the rectangle have so that its area is a maximum, and what is the maxuimum area?
= 2x*y= 2x*sqrt(25-x^2)
Now, take that, differentiate it, set to zero, and solve for x,y. Length = 2x, width (or height) is y.
I will be happy to critique your work or thinking.