A rectangle is inscribed in the region bounded by the -axis and the graph of in the…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A rectangle is inscribed in the region bounded by the

x

-axis and the graph of

y=9-x^{2}

in the first quadrant so that one side of the rectangle lies on the

x

-axis and the upper vertices lie on the curve. Let

(x,9-x^{2})

be the upper-right vertex of the rectangle. For which value of

x

is the area of the rectangle greatest? (a)

\sqrt{3}

(b)

\sqrt{2}

(c)

2

(d)

\sqrt{\dfrac{3}{2}}