The curve for bounds a region in the first quadrant

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The curve y=12−3x2y=12-3x^{2} for x≥0x\ge 0 bounds a region in the first quadrant. A rectangle has one vertex at the origin, vertices on the axes, and its upper-right vertex on the curve. For which xx-value is the area of the rectangle maximized? (a) x=32x=\sqrt{\dfrac{3}{2}} (b) x=43x=\sqrt{\dfrac{4}{3}} (c) x=2x=2 (d) x=43x=\dfrac{4}{3}

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