← OptimisationQuestion 2 of 16 · AS91578

A

A Dunedin packaging line makes open-top boxes from 40 cm × 40 cm squares of card by cutting a square of side x cm from each corner and folding up the sides. The volume of a box is V = (40 − 2x)²x cm³, for 0 < x < 20.

Only your final answer is marked, not your working.

A(a) Find the value of x that gives the greatest volume. You may assume this gives a maximum.

A(b) Find the greatest volume.