The total cost in dollars to produce q units of a product is c(q). fixed costs are $13000 . the marginal cost is c'(q)=0.006q^2-q+50.

estimate c(170) , the total cost to produce 170 units. find the value of c'(170). then combine these to find c(171).

C(q) = ∫C'(q) dq = ∫(0.006q^2 - q + 50)dq = 0.002q^3 - 1/2q^2 + 50q + c; where c = 13,000
C(170) = 0.002(170)^3 - 1/2(170)^2 + 50(170) + 13000 = 9826 - 14450 + 8500 + 13000 = $16,876
C'(170) = 0.006(170)^2 - 170 + 50 = 173.4 - 120 = $53.40

Therefore, C(171) = C(170) + C'(170) = $16,876 + $53.40 = $16929.40