Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides.

a) Write an expression for the volume V. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.
b) Use the given information to write an equation that relates the variables and then write the volume as a function of x.
c) Find the largest volume that such a box can have.

Question

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides.

a) Write an expression for the volume V.  Let x denote the length of the side of the square being cut out. Let y denote the length of the base.
b) Use the given information to write an equation that relates the variables and then write the volume as a function of x.  
c) Find the largest volume that such a box can have.