The cost of making $x$ units is $C(x) = x^{3} - 12x^{2} + 60x + 50$ rupees. At what output is the marginal cost least?

4 unitsCorrect answerYour answer5 unitsCorrect answerYour answer8 unitsCorrect answerYour answer12 unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$MC = 3x^{2} - 24x + 60$ , and $\frac{d}{dx}MC = 6x - 24$ .
This is 0 at $x = 4$ , and the second derivative 6 is positive: the least marginal cost is at 4 units (where $MC = 12$ ).

Worth noting

12 is the least value of the marginal cost, not the output where it occurs.

Ten questions from Rate of Change, Marginal Cost & Revenue, at your own pace.

Ten questions from Rate of Change, Marginal Cost & Revenue, at your own pace.

The cost of making xxx units is C(x)=x3−12x2+60x+50C(x) = x^{3} - 12x^{2} + 60x + 50C(x)=x3−12x2+60x+50 rupees. At what output is the marginal cost least?