Here's a picture of a rectangle inscribed in the first quadrant under the graph of [math]f(x) = 25 - x^2[/math]. Click and drag the upper-right corner of the rectangle to see the area and perimeter of the rectangle change.
[list] [*]What dimensions of the rectangle give the greatest area? [*]What dimensions give the greatest perimeter? [*]What dimensions give the greatest combined area and perimeter? [/list]