Final answer:
The cost function, given the marginal cost function C'(x) = 6x - 2 and the fixed cost of $11, is C(x) = 3x^2 - 2x + 11.
Step-by-step explanation:
To find the cost function, given the marginal cost function C'(x) = 6x - 2 and the fixed cost of $11, we need to integrate the marginal cost function. Integration will provide us the total cost function, C(x), except for the constant of integration, which in this case is the fixed cost.
Integrating the marginal cost function, we get:
- \(\int (6x - 2) dx = 3x^2 - 2x + C\)
Where C represents the constant of integration. Here, the fixed cost given is $11, so that will be our integration constant.
Therefore, the cost function C(x) is:
This function represents the total cost for producing x units, including the fixed cost and the variable cost represented by the integral of the marginal cost.