68. Inscribing a Rectangle Under a Parabola
A rectangle is inscribed between the x-axis and the parabola y=36−x2 with one side along the x-axis, as shown in the figure below.
(a) Let x denote the x-coordinate of the point highlighted in the figure. Write the area A of the rectangle as a function of x.
(b) What values of x are in the domain of A ?
(c) Sketch a graph of A(x) over the domain.
(d) Use your grapher to find the maximum area that such a rectangle can have.