Volume of a box

Question

A piece of cardboard measuring 8 inches by 12 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

v(x) = (8 - 2x)(12 - 2x)(x)

 

Multiply out, differentiate for maximum.