CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
A firm's total cost is C(x) = x³ − 12x² + 60x (in ₹), where x is output. At what output is marginal cost minimum?
Marginal cost is 3x² − 24x + 60. To minimise it, set its derivative 6x − 24 equal to zero, giving x = 4. The second derivative is positive, confirming a minimum of marginal cost at 4 units.
- Ax = 4Correct
- Bx = 6
- Cx = 2
- Dx = 10
Explanation
MC = 3x² − 24x + 60. Setting d(MC)/dx = 6x − 24 = 0 gives x = 4. The second derivative of MC is 6, which is positive, so MC is minimum. Setting MC = 0 gives no real root, so x = 6 or x = 2 do not arise from that route.
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