To find the marginal cost function, we need to differentiate the cost function $C(x)$ with respect to $x$.

The given cost function is: $C(x) = 4000 + 2x$

Step 1: Differentiate $C(x)$

The marginal cost function, $C'(x)$, is the derivative of $C(x)$ with respect to $x$.

$C'(x) = \frac{d}{dx}(4000 + 2x)$

Step 2: Apply the derivative

Since 4000 is a constant, its derivative is 0. The derivative of $2x$ is simply 2.

$C'(x) = 0 + 2 = 2$

Therefore, the marginal cost function is: $C'(x) = 2$

Answer

The correct answer is: b. $C'(x) = 2$

Would you like a more detailed explanation, or do you have any questions?

Here are some related questions to further your understanding:

1. How would you interpret the marginal cost function in a real-world business context?
2. What is the economic significance of having a constant marginal cost?
3. How does the revenue function's derivative compare to the marginal cost function?
4. How would you find the profit function using the given cost and revenue functions?
5. What does it mean if the revenue function has a decreasing marginal revenue?

Tip: The marginal cost function represents the additional cost incurred by producing one more unit of a product.