Math Problem Statement
Solution
To find the marginal cost function, we need to differentiate the cost function with respect to .
The given cost function is:
Step 1: Differentiate
The marginal cost function, , is the derivative of with respect to .
Step 2: Apply the derivative
Since 4000 is a constant, its derivative is 0. The derivative of is simply 2.
Therefore, the marginal cost function is:
Answer
The correct answer is: b.
Would you like a more detailed explanation, or do you have any questions?
Here are some related questions to further your understanding:
- How would you interpret the marginal cost function in a real-world business context?
- What is the economic significance of having a constant marginal cost?
- How does the revenue function's derivative compare to the marginal cost function?
- How would you find the profit function using the given cost and revenue functions?
- 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.
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Math Problem Analysis
Mathematical Concepts
Differentiation
Marginal Cost
Calculus
Formulas
Marginal cost function C'(x) = dC(x)/dx
Theorems
-
Suitable Grade Level
Undergraduate (Introductory Calculus)
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