If the average cost function of producing and marketing x units of an item is \(AC=2x-11+\displaystyle\frac{50}{x}\), then the marginal cost function is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(4x-11\)
Total cost = average cost × number of units:
\( \displaystyle C = x\cdot AC = x\left(2x - 11 + \frac{50}{x}\right) = 2x^2 - 11x + 50 \)
The marginal cost is the derivative of the total cost:
\( \displaystyle MC = \frac{dC}{dx} = 4x - 11 \)
Why the other options are incorrect
Option (1) \(2x^2-11x+50\) — Incorrect. This is the total cost C itself, before differentiating.
Option (2) \(2-\displaystyle\frac{50}{x^2}\) — Incorrect. This is the derivative of the average cost; MC is the derivative of the total cost.
Option (4) \(4x+39\) — Incorrect. The fixed cost 50 is a constant and disappears on differentiation; it cannot be added to 4x − 11.