A sheet of cardboard is to be turned into an open-top box by cutting squares of side…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

20\text{ cm}\times30\text{ cm}

sheet of cardboard is to be turned into an open-top box by cutting squares of side length

x

centimeters from each corner and folding up the sides. For

0<x<10

, which value of

x

produces the box with the greatest volume? (a)

x\approx6.2\text{ cm}

(b)

x=5\text{ cm}

(c)

x\approx3.9\text{ cm}

(d)

x=2\text{ cm}