Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in dollars) given by the function S′(x)​, where x is the number of years of operation of the​ machine, while producing a rate of annual costs​ (in dollars) given by the function C′(x).   S'(x)=212-x2, C'(x)=x2+6/5 x   a. For how many years will it be profitable to use this new​ machine? b. What are the net total savings during the first year of use of the​ machine? c. What are the net total savings over the entire period of use of the​ machine?

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