Final answer:
To find the cost function from the marginal cost function C'(x) = 20x - 9, integrate to get C(x) = 10x^2 - 9x + 12, including the fixed cost of $12.
Step-by-step explanation:
The student's question involves finding a cost function given a marginal cost function and a fixed cost. To find the cost function, we integrate the marginal cost function. The marginal cost function is given as C'(x) = 20x - 9. After integrating, the cost function will have the form C(x) = ax^2 + bx + c, where 'a' and 'b' are constants derived from integration and 'c' is the fixed cost. Therefore, integrating 20x gives us 10x^2, integrating -9 gives us -9x, and then we add the fixed cost of $12. The complete cost function is C(x) = 10x^2 - 9x + 12.