5. (18%) The production cost (dollars) of a certain product is given by f (x) = xe"'-01x +2, where x is the number of unit of products produced (For this problem, x can be considered a continuous variable so that f can be differentiated. In a practical application, you can always round your final calculated result in a whole unit if that would make more practical sense; e.g., rounding x=0.85 as x=1 unit). (a) Show that the marginal cost of the production is a decreasing function of x (the marginal cost is simply the derivative of the production cost function, f. You can read the textbook (Sect. 2.1) for the definition of the marginal cost). (b) Determine the number of units that must be produced when the saving on marginal cost is no more than $0.05 per unit. 5. (18%) The production cost (dollars) of a certain product is given by f (x) = xe"'-01x +2, where x is the number of unit of products produced (For this problem, x can be considered a continuous variable so that f can be differentiated. In a practical application, you can always round your final calculated result in a whole unit if that would make more practical sense; e.g., rounding x=0.85 as x=1 unit). (a) Show that the marginal cost of the production is a decreasing function of x (the marginal cost is simply the derivative of the production cost function, f. You can read the textbook (Sect. 2.1) for the definition of the marginal cost). (b) Determine the number of units that must be produced when the saving on marginal cost is no more than $0.05 per unit