Using U.S. Census Bureau data since 1870, the average number of acres per U.S. farm can be modeled with the function
A(t) = -0.000377t3 + 0.1021t2 - 4.731t + 174.3
where t is the number of years past 1870.
(a) Find the years when the model has a relative maximum and a relative minimum.
(b) What changes in our society and in the economy during the last half of the 20th century have caused A(t) to increase then?