Calc
posted by Manny .
A rectangle is inscribed with its base on the xaxis and its upper corners on the parabola y= 1x^2. What are the dimensions of such a rectangle with the greatest possible area?

let the point of contact of the top right corner with the parabola be (x,y)
then the base of the rectangle is 2x and its height is y
Area = 2xy
= 2x(1  x^2)
= 2x  2x^3
D(area)/dx = 2 = 6x^2
= 0 for a max of area
solve for x , then find y ...
very easy from here on