8.4 Challenging Integral Applications
Economics & Biology Applications
Question #1 (Easy): Marginal Cost Function Using the Net Change Theorem
Net Change Theorem is practical approach that is equivalent to the Fundamental Theorem of Calculus
Part 2. Thus, given the marginal rate function, first take the integral to find the anti-derivative, then plug
in the net change values as the beginning and end points to determine the total cost over the interval.
Marginal cost function of publishing copies of books is given by ( ) ,
where is in thousands, as well as the cost is in thousands of dollars. The fixed start-up cost is .
1) What is the cost of publishing the first copies of the book?
2) What about the next copies?
1) First, since the marginal cost function is provided, the total cost function needs to be
determined. This is simply the anti-derivative of ( ). To find the cost from to , noting
that is in