Question: An efficiency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 8am will have produced \(Q\left( t \right)=-{{t}^{3}}+\frac{9}{2}{{t}^{2}}+12t\) units t hours later.

(a) Compute the worker’s rate of production with respect to time t.

(b) At what rate is the worker’s rate of production changing with respect to time at 9am

(c) Use approximation to estimate the change in the workers’ rate of production between 9am and 9:06am, and compute the actual change in the rate of production.