6. A rectangle is to be drawn so its base is on the ( x ) axis, its left side is on the ( y ) axis, and the upper right vertex is on the parabola given by ( y=12-x^{2} ).
(a) (10) Draw a sketch of this situation, and find a formula for the area ( A ) as a function of the length of the base. (Don't forget to include the domain of ( A ) !)
(b) (15) Then determine the area ( A ) of the rectangle that is as large as possible, identify the upper right vertex of that rectangle, and justify your answer as the maximum possible area.