Question 1030320
The cost function would be the integral of the marginal cost function:

{{{C(x) = int((x^(1/3) +6), dx) = (3/4)x^(4/3) + 6x + k}}} for some undetermined constant k.

Since C(8) = 112, we have {{{C(8) = 112 =  (3/4)8^(4/3) + 6*8 + k = 12+48+k}}}

==> k = 52.

Therefore {{{C(x) = (3/4)x^(4/3) + 6x + 52}}}