Question: The total cost \(C\left( x \right)\) incurred by the On-Time Watch Company at one of its plants during a given day is given by \(C\left( x \right)=1500+30x+{{x}^{2}},\,\,0\le x\le 75\), where \(x\) is the number of watches produced

(a) What is the average cost On-Time incurs in manufacturing fifty watches at this plant in one day?

(b) Find \(C'\left( x \right)\)

(c) What is the rate of change in the total cost when the level of production is 15 watches per day?

(d) What is the approximate cost of producing the 16^th watch?