# Marginal cost- i've never done these types of problems before and very confused

1. Oct 23, 2011

### jtt

1. The problem statement, all variables and given/known data
suppose that the dollar cost of producing x washing machines is c(x)= 2000 + 100x-0.1x6^2

a) find the average cost of producing 100 washing machines.
b) find the marginal cost when 100 washing machines are produced.

2. Relevant equations
c(x)= 2000 + 100x-0.1x6^2: the only equation given

3. The attempt at a solution
i've tried taking the derivative and then substituting it with 100. for part a and for part b i didnt take the derivative, just plugged in 100 into the equation given

2. Oct 23, 2011

### dynamicsolo

Could you clarify that cost function expression? Is it $c(x) = 2000 + 100x - 0.1x^{2}$?

The total cost to produce 100 washing machines is c(100) . The average cost is the cost per machine, which is $\frac{ c(100) }{100} .$

The marginal cost, on the other hand, is the linearization for finding the amount of additional cost it would take to produce one more machine, given that 100 have already been built. This linearization is $c'(100) \cdot ( 101 - 100 )$ , or just c'(100) .

3. Oct 23, 2011

### jtt

yes the cost function expression is c(x)= 2000 + 100x-0.1x^2

4. Oct 23, 2011

### dynamicsolo

Well, the definitions I've given are all you need. You started doing some calculations along those lines, but I think you had some of what you needed to do swapped relative to which part it goes with.

5. Oct 23, 2011

### jtt

thanks for the help on this