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Rate of Change, Marginal Cost & Revenue · Question 42 of 79

At what daily output is the factory's marginal cost lowest?

Question 42

MediumOriginal question

A factory's cost of making xx radios a day is C(x)=500+40x−0.6x2+0.01x3C(x) = 500 + 40x - 0.6x^{2} + 0.01x^{3} rupees.

At what daily output is the factory's marginal cost lowest?

Options for question 42

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. ddx(MC)=−1.2+0.06x=0\frac{d}{dx}(MC) = -1.2 + 0.06x = 0 at x=20x = 20.

  2. The next derivative, 0.06, is positive, so this is a minimum.

Worth noting

40 radios differentiates 0.03x20.03x^{2} as 0.03x0.03x.

Concept
The lowest point of marginal cost
Typical time
120 s
Your time
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The rule this testsMarginal cost
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