Question

A piece of cardboard measuring 13 inches by 14 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides.

Find a formula for the volume of the box in terms of x
V(x)=

Find the value for x that will maximize the volume of the box
x=

Answer 1

dimensions of the base of the box will be (13-2x) and (14-2x)
the height would be x

so the volume = x(13-2x)(14-2x)

expand, differentiate that expression with respect to x,
set it equal to zero for a max of volume and solve for x
let me know what you get