I attempted to solve this problem. I just want to make sure that I did it properly.

The parabola is y=8-x^2

Rectangle = 2x(8-x^2)

=16-6x^2 (i got this by first distributing 2x then finding the derivative)

X= Sqrt(8/3)

Since the base is 2x, the base of this rect. would be 2Sqrt(8/3)

then since y is a f(x). I get 16/3

The dimensions of my rectangle would be H= 16/3 and L = 2Sqrt(8/3)

My area would be 17.42

Thank you!