A company designs spinning toys using the family of functions y = cx 4 − x 2 , where c is a positive
constant. The figure above shows the region in the first quadrant bounded by the x-axis and the graph of
y = cx 4 − x
2 , for some c. Each spinning toy is in the shape of the solid generated when such a region is
revolved about the x-axis. Both x and y are measured in inches.