In business calculus, if total cost is given by $C\left(x\right)$ where $x$ is the number of units produced, what does marginal cost refer to?

• A. The total cost at a specific production level, $C\left(x\right)$, representing the overall cost of producing $x$ units
• B. The total cost divided by the number of units, $\frac{C\left(x\right)}{x}$, representing average cost per unit
• C. The derivative of total cost with respect to output, $\frac{dC}{dx}$, representing the approximate cost of producing one additional unit
• D. The change in output per change in cost, $\frac{dx}{dC}$, representing how production responds to spending

Answer: (C)

Verified step by step guidance

1. Understand that the total cost function \(C(x)\) represents the overall cost of producing \(x\) units of a product.
2. Recognize that average cost is calculated by dividing the total cost by the number of units, expressed as \(\frac{C(x)}{x}\), which gives the cost per unit on average.
3. Identify that marginal cost is related to how the total cost changes as production changes, specifically focusing on the cost of producing one more unit.
4. Express marginal cost mathematically as the derivative of the total cost function with respect to the number of units produced, written as \(\frac{dC}{dx}\).
5. Interpret this derivative \(\frac{dC}{dx}\) as the approximate additional cost incurred when increasing production by one unit, which is crucial for making production decisions.