Answer
maximum area $A=17.419$ at $x=1.833, y=4.640$
Work Step by Step
1. As shown in the figure of the problem, the base width of the rectangle is $2x$ and the height is $y$ with $(x,y)$
satisfying the equation $y=8-x^2$. The area (A) of the rectangle is given by $A=2xy=2x(8-x^2)=-2x^3+16x$
2. Graph the above function as shown in the figure. A maximum can be found at $x=1.833, A=17.419$ at this
$x$ value, $y=8-1.833^2=4.640$
