Question

A box is made from two identical square sheets of metal with edge length L. A small square of edge length x is removed and the two flaps are folded up. Find the value of x that maximizes the volume of the box.

Answer 1

Edge length of square =L

A small square of edge length x

Length of box =L-2x

Width of box =L-2x

height of box =x

now, we can find volume

now, we can find derivative

now, we can set it to 0

and then solve for x

and we get

............Answer