Posted by **Manny** on Sunday, April 5, 2009 at 1:51pm.

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

- Calc -
**Reiny**, Sunday, April 5, 2009 at 2:06pm
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

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