Suppose that a particular industrial machine, when it is t years old, generates revenue at the rate R′(t)=7975−6t^2 dollars per year and that operating and servicing costs accumulate at the rate C′(t)=3400+20t^2 dollars per year.
How many years pass before the profitability of the machine begins to decline?
Compute the net profit generated by the machine over its useful lifetime.