In business calculus, marginal cost is interpreted as a derivative. What does marginal cost refer to?

• A. The total cost of producing exactly $q$ units, $C\left(q\right)$.
• B. The rate of change of quantity with respect to total cost, $\frac{dq}{dC}$.
• C. The average cost per unit, $\frac{C\left(q\right)}{q}$.
• D. The rate of change of total cost with respect to quantity produced, $\frac{dC}{dq}$.

Answer: (D)

Verified step by step guidance

1. Understand that in business calculus, the total cost function is denoted as \(C(q)\), where \(q\) represents the quantity of units produced.
2. Recognize that marginal cost is related to how the total cost changes as the quantity produced changes, which means it involves the concept of a derivative.
3. Recall that the derivative of the total cost function with respect to quantity, written as \(\frac{dC}{dq}\), measures the instantaneous rate of change of cost when producing one more unit.
4. Interpret this derivative \(\frac{dC}{dq}\) as the marginal cost, which tells us the additional cost incurred by producing one extra unit of the product.
5. Distinguish marginal cost from other concepts such as total cost \(C(q)\), average cost \(\frac{C(q)}{q}\), and the incorrect rate of change \(\frac{dq}{dC}\), confirming that marginal cost is specifically \(\frac{dC}{dq}\).