Question

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.

Answer 1

Answer:

$C(x) = \frac{x^4}{4}-3x^2+3,000$

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:

$C(x) = \int\ {C'(x)} \, dx \\C(x) = \int\ {(x^3-6x)} \, dx \\C(x) = \frac{1}{4} x^4-3x^2+a$

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

$C(x) = \frac{x^4}{4}-3x^2+3,000$