By using U.S. Department of Energy data for selected years from 2011 and projected to 2040, the U.S. onshore oil reserves in the lower 48 states (in billions of barrels) can be modeled by the

Function R(t)=-0.00044t3+0.0042t2+0.52t+19 where t is the number of years past 2010.

(a) In what year does the model predict the onshore oil reserves in the lower 48 states will reach a maximum? Find the predicted maximum. Is this the absolute maximum for the period from 2011 to 2040?

(b) Find the absolute minimum point for the period from 2011 to 2040.

(c) Find the t-value of the point of inflection for R(t) At that t-value, is the rate of change of these oil reserves maximum or minimum? Explain.