A rectangle has its two lower corners on the x-axis and its two upper corners on the curve...

I'll answer only the first question because im sure about it
Assume the dimensions are Y and 2X
then , the Area = 2xy   , since  y = 16 - x^2
then we can write A = 2 x ( 16 - x^2 ) = 32x - 2 x^3
find the derivative  A' = 32 - 6 x^2  and then find the zeros of the derivative
32 - 6 x^2 = 0   >> x = +/- 2.3  , since he asks for the largest area then we can notice that 2.3 is a local maximum ( or it is obvious that you should take the postive value because it is dimensions )
so x = 2.3   > y = 10.7     DIMENSIONS ARE  2x = ((4.6 ))and y = ((10.7 ))

Solution provided below...