CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The total cost function of a firm is C(x) = 2x³ − 9x² + 50x + 400, where x is the number of units produced. What is the marginal cost when 3 units are produced?
Marginal cost is the derivative of total cost. Differentiating gives 6x² − 18x + 50, and at x = 3 this equals 54 − 54 + 50 = ₹50.
- A₹23Correct
- B₹50
- C₹77
- D₹14
Explanation
Marginal cost = dC/dx = 6x² − 18x + 50. At x = 3: 6(9) − 54 + 50 = 54 − 54 + 50 = 50. Re-check: 6×9 = 54, 18×3 = 54, so MC = 50. So the correct value is ₹50, and option 1 is the key, not option 0.
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