I have a rectangle inscribed in the parabola defined by
$\displaystyle y=8-x^2$ with one edge on the x-axis ?
Would I assume that edge on the x-axis is x or 2x?
So i'm guessing you're trying to maximize your area?
$\displaystyle A = 2x(8 - x^2) = 16x - 2x^3$
$\displaystyle A' = 16 - 6x^2$
$\displaystyle 0 = 16 - 6x^2$
$\displaystyle 16 = 6x^2$
$\displaystyle x = \sqrt \frac{16}{6}$
Seeing as we can't have negative dimensions, we use +.