A piece of cardboard measuring 12 inches by 13 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides.

Question

A piece of cardboard measuring 12 inches by 13 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) = (12 - 2x)(13 - 2x)(x)

Determine V'(x) and set equal to 0.