A square sheet of cardboard with side length is to be made into an open-top box by…

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

Problem

A square sheet of cardboard with side length

24\text{ in}

is to be made into an open-top box by cutting equal squares of side

x

inches from each corner and folding up the sides. For which value of

x

is the volume of the box greatest? (a)

8\text{ in}

(b)

2\text{ in}

(c)

4\text{ in}

(d)

6\text{ in}