Chapter 9.1, Problem 59E

Productivity During an 8-hour shift, the rate of change of productivity (in units per hour) of infant activity centers assembled after t hours on the job is

$r(t)=\frac{128(t^2+6t)}{{(t^2+6t+18)}^2},0\le t\le 8$

(a) Find $\underset{t\to 4}{\lim }r(t)$.

(b) Find $\underset{t\to 8^{-}}{\lim }r(t)$.

(c) Is the rate of productivity higher near the lunch break (at t = 4) or near quitting time (at t = 8)?