Mathematics

Mathematics

Problem

A rectangle is inscribed in the region bounded by the xx-axis and the graph of y=9−x2y=9-x^{2} in the first quadrant so that one side of the rectangle lies on the xx-axis and the upper vertices lie on the curve. Let (x,9−x2)(x,9-x^{2}) be the upper-right vertex of the rectangle. For which value of xx is the area of the rectangle greatest? a) 3\sqrt{3} b) 2\sqrt{2} c) 22 d) 32\sqrt{\dfrac{3}{2}}

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