An open rectangular box is to be made from a piece of cardboard 8 in. wide and 15 in. long by cutting a square from each corner and bending
up the sides. Find the dimensions of the box of largest volume.

Question

An open rectangular box is to be made from a piece of cardboard 8 in. wide and 15 in. long by cutting a square from each corner and bending
up the sides. Find the dimensions of the box of largest volume.

anonymous · Answer

the volume will be 
$$V(x)=x(15-2x)(8-2x)$$ multiply out, take the derivative, find the critical points by setting the derivative equal to zero and solve