For , a solid has rectangular cross sections perpendicular to the x-axis. At each ,…

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

Problem

For

0\le x\le 1

, a solid has rectangular cross sections perpendicular to the x-axis. At each

x

, the rectangle has width

k x

centimeters and height

(6-kx)

centimeters, where

k

is a positive constant less than 6. For what value of

k

(in centimeters

^{-1}

) is the volume of the solid maximized? (a)

k=3

(b)

k=4.5

(c)

k=1.5

(d)

k=6