Problem $2(5$ points$)$: A rectangle is inscribed in the parabola $y=108-x^2$ with its base on the $x-$axis and its two upper corners on the parabola. Find the dimensions that maximize the area of the rectangle.

Problem $3(5$ points$)$: Find the point on the curve $y=8\sqrt[\phantom{2}]{x}$ that is closest to the point $(36,0)$