The total cost of producing q units is C(q) = q^2 - 12q + 100. For q > 0, at what output is average cost minimised?
Correct answer: B. 10 units
- A. 8 units
- B. 10 units
- C. 12 units
- D. 14 units
Explanation
Average cost is C(q)/q = q - 12 + 100/q. Its derivative is 1 - 100/q^2, which is zero at q = 10, giving the minimum average cost.
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About Differentiation and Optimisation
Differentiation covers gradients, standard derivative rules, the product and quotient rules, the chain rule, stationary points and rates of change. Optimisation uses first and second derivatives to classify maxima and minima, while applications include tangent and normal lines, marginal quantities and related rates.
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