A piece of cardboard measuring 14 inches by 11 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 14 inches by 11 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) = x(14 - 2x)(11 - 2x)

Expand

Differentiate and set equal to zero.