Written assignment 4, due on Mar 21stPlease make sure to provide good reasoning to all steps of your work. Full sentences are expected.This exercise is about a hypothetical factory and not based on real industries.A factory can produce between 0 and 10 tons of products per day. However, for producing x tons of products in one day, it will emit e53 tons of CO2.(a) Find the function f(x) that describes CO2 emissions per product production. For example if one day 2 t of product are produced and 8 t of CO2 get emitted, the emission per product is 4, i.e.f(2)=4.(b) What daily production leads to minimal carbon emissions per product?If you are unsure about your result from part (a), you can do the remaining exercises with f(x)=9cx-2x3 instead. In this case please clearly state this on your submission.(c) Use intercepts, asymptotes and intervals of increase/decrease to sketch an approximate graph of f(x).(Like for all exercises, make sure you explain your reasoning)(d) How would you interpret the graph of f(x) with respect to the emissions per product?