CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The total cost of a firm is C(x) = x³ − 6x² + 20x + 500. The rate of change of marginal cost with respect to output is zero at x equal to:
The rate of change of marginal cost is zero at x = 2. Marginal cost is 3x² − 12x + 20, and its derivative is the second derivative of cost, 6x − 12. Equating this to zero gives x = 2.
- A1
- B2Correct
- C4
- D6
Explanation
Marginal cost MC = C'(x) = 3x² − 12x + 20. Its rate of change is C''(x) = 6x − 12. Setting 6x − 12 = 0 gives x = 2. Setting MC itself to zero has no real root, and x = 4 would come from solving 3x² − 12x = 0.
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