Posted by
**Tezuka** on
.

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?

Area= length*width

= 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.