What are the dimensions of such a rectangle with the greatest possible area?

Question

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9−x2. What are the dimensions of such a rectangle with the greatest possible area?

width=

height=

Answer 1

width = 2sq3

height = 6

max area = 12sqr3

A = xy =x (9-x^2) = 9x - x^3

A' = 9 -3x^2

x^2 = 3

x = sqr3

y = 6