Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.

(c)Write an expression for the volume V in terms of both x and y.

V =

(d)Use the given information to write an equation that relates the variables x and y.

(e)Use part (d) to write the volume as a function of only x.

V(x) =

(f)Finish solving the problem by finding the largest volume (in ft³) that such a box can have.

V = ft³