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Question: If the value function of a certain item is defined by C(x) = 200 + 50 + 2x2, then find the marginal cost function.


A ) 2x50 + 2x2
B ) 2x2x2
C ) 25 +x2
D ) x50 + 2x2

Steps to derive

1 C(x) = 200 + 50 + 2x2 = 200 + (50+2x2)12

2 The marginal cost function is C ′(x) = ( 12) (50+2x2)-12(4x)
 [Use the general power rule and the chain rule.]

3 = 42x(50 + 2x2)-12

4 = 2x50 + 2x2
 [Simplify.]



Hence the right answer is Option A

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