CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The average cost function of a firm is AC = x + 10 + 400/x, where x is output. At what output is average cost minimum?
Differentiate average cost to get 1 − 400/x² and set it to zero. This gives x² = 400, so x = 20. The second derivative is positive, so average cost is minimum at 20 units.
- A10 units
- B40 units
- C20 unitsCorrect
- D400 units
Explanation
d(AC)/dx = 1 − 400/x² = 0 gives x² = 400, so x = 20. The second derivative 800/x³ is positive, confirming a minimum. Choosing 10 wrongly takes the square root of the constant 100.
Did you get it right without looking?
One question tells you little. A timed set on Differential and Integral Calculus shows your real accuracy, how long you take and where you lose marks.
More Differential and Integral Calculus questions
- The value of the definite integral of x·e^(2x) with respect to x from 0 to 1 is:
- Which of the following is the value of the definite integral of (4x³ − 2x) with respect to x from x = 1 to x = 3?
- If ∫ from 0 to k of (2x + 3) dx = 18, where k > 0, then the value of k is:
- The marginal cost of a firm is MC = 6x + 10 (in ₹), where x is the number of units. Increasing output from 2 units to 5 units raises total c…
- The indefinite integral of 1/x with respect to x, for x > 0, is:
- If y = x² eˣ, then the value of dy/dx at x = 1 is: