U.S. railroad miles the graph shows the number of miles of U.S. railroads for selected years from 1850 to 2006. Suppose that data can be modeled with the function
R(t) = 0.000062t3 - 0.046t2 + 6.55t - 25.6
where R(t) is thousands of miles of railroads and t is the number of years past 1850.
(a) Find the year in which the model indicates the number of railroad miles is maximum. Does this agree with the data?
(b) The data seem to be leveling off beyond 2000. For the year 2010, does R'(t) indicate that this is true for the model?