The volume (in cubic centimeters) of an open-top box formed by cutting congruent…

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

Problem

The volume (in cubic centimeters) of an open-top box formed by cutting congruent squares of side length

x

centimeters from each corner of a

20\text{ cm}\times 20\text{ cm}

square sheet of cardboard and folding up the sides is

V(x)=x(20-2x)^2

for

0<x<10

. For which value of

x

is the volume of the box greatest? (a)

4

(b)

\dfrac{10}{3}

(c)

2

(d)

5