In business calculus, marginal cost is best defined as the change in which quantity with respect to output quantity $q$?

• A. Total cost $C$ with respect to output: $\frac{dC}{dq}$
• B. Average cost with respect to output: $\frac{d(\frac{C}{q})}{dq}$
• C. Profit $P$ with respect to output: $\frac{dP}{dq}$
• D. Total revenue $R$ with respect to output: $\frac{dR}{dq}$

Answer: (A)

Verified step by step guidance

1. Understand that marginal cost in business calculus refers to the rate at which total cost changes as the output quantity changes.
2. Identify the total cost function, denoted as \(C\), which depends on the output quantity \(q\).
3. Express marginal cost mathematically as the derivative of the total cost function with respect to output quantity: \(\frac{dC}{dq}\).
4. Recognize that this derivative represents the instantaneous change in total cost for a very small change in output quantity.
5. Note that marginal cost is not the derivative of average cost, profit, or total revenue with respect to output, but specifically the derivative of total cost.