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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. :D
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.