Mathematics

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

k=4.5

k=1.5

k=6