Apentix/AP Calculus AB/Unit 4: Contextual Applications of Differentiation/Question

AP Calculus ABmediummcq1 pt

The cost in dollars of producing $x$ items is $C(x)=0.1x^3-2x^2+20x+500$ . What is the marginal cost at $x=10$ items?

A.

C(10)=600

dollars, the total cost of producing 10 items.

B.

C'(10)=30

dollars per item.

C.

C'(10)=20

dollars per item.

D.

C'(10)=10

dollars per item, the approximate cost of producing the 11th item.

Explanation

Core Concept

Marginal cost is $C'(x)=0.3x^2-4x+20$ . At $x=10$ this is $30-40+20=10$ dollars per item.

Correct Answer

D $C'(10)=10$ dollars per item, the approximate cost of producing the 11th item.

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