A company determined that the marginal cost, C' (x )of producing the xth unit of a product is given by C' (x )= x^3- 6x. Find the total cost function C, assuming that C(x) is in dollars and that fixed costs are $3000.

Step-by-step explanation:

The marginal cost function, C'(x), is the derivate of the cost function, C(x).

Therefore, we can obtain the cost function by finding the integral of the marginal cost function:

Where 'a' is a constant and represents fixed costs. If fixed costs are $3,000, the cost function is: