Cost function

Question

A firm is able to determine that its marginal cost, in dollars, from producing x units of an item is given by C′(x)=2100x^-2.2, where x≥1. Suppose that it were possible for the firm to make infinitely many units of this item, what would its total cost be?

Answer 1

'c'(x) = 2100x^-2.2 = 2100/x^2.2 with x greater than or = 1

C(x) = integral of marginal cost = (2100/-1.2)x^-1.2 = -2100/1.2x^1.2 Using the power rule

as x goes to infinity, both C(x) and C'(x) approach zero

this isn't a very realistic problem. such a model doesn't exist in the real world