CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The total cost function of a firm is C(x) = 0.1x² + 20x + 500 (in ₹), where x is the number of units produced. The marginal cost at an output of 30 units is:
Marginal cost is the derivative of the total cost function, giving MC = 0.2x + 20. Substituting x = 30 gives 6 + 20 = ₹26, so the marginal cost at 30 units is ₹26.
- A₹26Correct
- B₹23
- C₹29
- D₹56
Explanation
Marginal cost is the derivative of total cost: MC = dC/dx = 0.2x + 20. At x = 30, MC = 0.2(30) + 20 = 6 + 20 = ₹26. The value ₹23 comes from wrongly using 0.1x instead of 0.2x.
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