The marginal cost of manufacturing an item when x thousand items are produced is dc/dx= 4x^3 - 6x + 5 dolars/item. find the cost function c(x) if c(0)=550

The cost function is .

Step-by-step explanation:

It is given that the marginal cost of manufacturing an item when x thousand items are produced is

We need to find the cost function.

Multiply both sides by dx.

Integrate both sides to find the cost function.

where, C(x) is const function and C is a constant.

It is given that C(0)=550. Substitute x=0 in the above function.

Therefore, the cost function is .