Suppose the total cost function, in dollars, for the production of x units of a product is given by C(x) = 4000 + 55x + 0.1x2. Then the average cost of producing x items is %3D total cost 4000 + 55 + 0.1x = (x)- (a) Find the instantaneous rate of change of average cost with respect to the number of units produced. That is to say, find C' (x). (b) Find the level of production at which this rate of change equals zero. In other words, solve the equation C' (x) = 0. (c) At the x value found in part (b), find the instantaneous rate of change of cost and find the axerage cost WWhat do you notice?

The price p (in dollars) and the demand x for a particular clock radio are related by the equation x = 5000 – 50p. (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R? (C) Find the marginal revenue at a production level of 2800 clock radios. (D) Interpret R'(3900) = – 56.00.

The total profit of a company since it started a business is given by P(t) = .01t^3 + 10t − 15 where t is the number of months since the company started a business. (a) Find the total profit 11 months after the company started a business (b) Find the marginal profit of the 11th month.