Chapter 5.2, Problem 84E

Oil production. Assume that the rate in Problem 83 is found to be

     $\begin{array}{cc}R\left(t\right)=\frac{120t}{t^2+1}+3& 0\le t\le 20\end{array}$

(A)    When is the rate of production greatest?

(B)    How many barrels of oil Q(t) will the field produce in the first t years if Q(0) = 0? How many barrels will be produced in the first 5 years?

(C)    How long (to the nearest tenth of a year) will it take to produce a total of a quarter of a million barrels of oil?