Squares of side length inches are removed from each corner of a -inch by -inch…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Squares of side length

x

inches are removed from each corner of a

18

-inch by

24

-inch rectangular sheet of metal, and the sides are folded up to form an open-top box. For

0<x<9

, determine the value of

x

that yields the maximum volume of the box. Give your answer exactly.