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Question: Which of the following will be the cost function for the marginal cost function C′(x) = 1(x + 1); fixed cost is $18.


A ) C(x) = - ln|x + 1| + 18
B ) C(x) = ln|x - 1| + 18
C ) C(x) = ln|x + 1| + 18
D ) C(x) = ln|x + 1| - 18

Steps to derive

1 C′(x) = 1x + 1
 [Given.]

2 Since fixed cost is $18, C(0) = 18.

3 C(x) = ∫1x + 1dx
 [Integrate both sides of the given differential equation.]

4 C(x) = ln|x + 1| + C

5 18 = ln1 + C
 [Substitute x = 0, C(0) = 18.]

6 C = 18

7 Thus, the cost function is C(x) = ln| x + 1| + 18.



Hence the right answer is Option C

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