SOLUTION: Find the cost function if the marginal cost function is given by C`(x)=(x^1/3) +6 and 8 units cost $112. C(x)=

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Question 1030320: Find the cost function if the marginal cost function is given by C`(x)=(x^1/3) +6 and 8 units cost $112.
C(x)=

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The cost function would be the integral of the marginal cost function:
for some undetermined constant k.
Since C(8) = 112, we have C%288%29+=+112+=++%283%2F4%298%5E%284%2F3%29+%2B+6%2A8+%2B+k+=+12%2B48%2Bk
==> k = 52.
Therefore C%28x%29+=+%283%2F4%29x%5E%284%2F3%29+%2B+6x+%2B+52