Find the dimensions of a square box, with fixed surface area 6
square feet, that maximize the volume of the box using the
following steps:
1. Express the surface area of
the box in terms of x, the dimension of one side of the base, and
the height h. Then solve for h in terms of x.
2. Find a formula for the
volume V , in terms of x.
3. Take the derivative of the
volume function and set it equal to zero to solve for the critical
points. There are two critical points, but only one can be the
value of x (Why?). Use this value to find h.