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To find the marginal cost function \( C'(x) \), we need to differentiate the given cost function \( C(x) = 178 + 1.8x \).

The marginal cost is simply the derivative of the cost function:

\[
C'(x) = \frac{d}{dx}(178 + 1.8x)
\]

1. The derivative of a constant, like 178, is 0.
2. The derivative of \( 1.8x \) with respect to \( x \) is just \( 1.8 \).

Thus, the marginal cost function is:

\[
C'(x) = 1.8
\]

Would you like more details or further explanation?

Here are five follow-up questions you might consider:
1. What is the significance of the marginal cost in economics?
2. How do you interpret the constant marginal cost in this case?
3. Can the marginal cost ever be negative, and what would that mean?
4. How would you compute total cost if you know the marginal cost function over time?
5. What other types of cost functions could exist, and how might their marginal costs differ?

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

Find the marginal cost function. C(x) = 178 + 1.8x

This problem involves finding the marginal cost function by differentiating C(x) = 178 + 1.8x. The solution shows the application of calculus, specifically the derivative of linear functions. This is ideal for high school or undergraduate students learning about marginal costs.

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