Who is asking: Student Level: Secondary
If C(x) is the cost function where x is the level of production of the product being produced them the marginal cost, MC(x), is the derivative of C(x). Thus, using antidifferentiation you can find the cost function. Since
You are also told that the the fixed costs are $100, in other words C(0) = $100. Thus
In a similar way you can find the revenue function, M(x), since M'(x) = MR(x). In this case, if you produce no product the revenue is $0 and hence R(0) = 0.
The profit function, P(x), is the revenue the cost, and hence