Exploring the Open-Top Box Problem

The left window controls the box's dimensions. The right window shows the volume for different values of x.
  1. Select the dimensions of the box (width, height) and then find the value of x that will maximize the volume.
  2. Write an equation for the volume of the box as a function of x.
  3. Select "show formula" in the right window to see if you were correct. (hide when finished)
  4. Repeat steps 1-3 a total of three times.
  5. Find the derivative of the equations from above and verify that the optimal value for the box's volume happens at the value for x that you found above.
Thanks to Simona Riva for creating this applet.