The maximum area of a rectangle with vertical sides and

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

Problem

The maximum area of a rectangle with vertical sides

x=x_0

and

x=\pi-x_0

, inscribed in the region bounded by

y=\sin x

and the

x

-axis, is obtained when

x_0\in

: (1)

\left(\frac{\pi}{4},\frac{\pi}{3}\right)

(2)

\left(\frac{\pi}{6},\frac{\pi}{4}\right)

(3)

\left(0,\frac{\pi}{6}\right)

(4) None of these