Thread: Computing the cost of manufacturing 20th unit

Suppose the total cost of manufacturing q units of certain commodity is given by

C (q) = q^3-30q^2+400q+500

a. Computer the cost of manufacturing 20 units.
I understand what to do here. Just plug in 20.

b. Compute the cost of manufacturing the 20th unit.
Isn't it c(20) -c (0) / 20 - 0 ???

Try c(20) - c(19)

How do you know it's 20 and 19?
Sorry I have a recitation tomorrow and odds are there are going to be word problems on the quiz. I'm just trying to understand it better.
Thanks so much again, TKHunny!

Well, it's "20" because you are asked about the 20th item! And it's "19" because a "unit" is one item and 19= 20- 1. Specifically, the total cost of manufacturing the first 19 is C(19) and the cost of manufacturing the first 20 is C(20). The difference, C(20)- C(19), is the cost of manufacturing just that last one.

The formula you gave, (C(20)- C(0))/20 is the average cost of manufacturing each of 20 items.