Math - Total cost and average cost? Alright so mainly I'll start with the question:

The total cost to produce x disks is

C(x) = 30 * sqrt( 1 - 0.9e^ (-1.2x) )

dollars.

a) Find the average cost if 100 disks are produced.

So mainly for this part i tried to do is:

Average C(100)
= 30 * sqrt( 1 - 0.9e^ (-1.2(100)) )
--------------------------------------...
..........................100


But i'm not sure if that's right, i thought that the average cost is equal to the total cost divided by x units

Then i'm stuck on these:

b) Find the marginal average cost if 100 disks are produced.

c) Explain what the amount computed in part (b) means

a.
AC = C / x (think about it as cost per unit)

C(x) = 30sqrt(1 - 0.9e^(-1.2x))
AC(x) = (30/x)sqrt(1 - 0.9e^(-1.2x))

We want to find AC(100) so simply plug in 100 for x and evaluate.

b.
MC = C'

C'(x) = 30[1/2sqrt(1 - 0.9e^(-1.2x)][-0.9e^(-1.2x)](-1.2)

Once again, you want to find C'(100) so plug in 100 for x, then simplify and evaluate.

c.
Think about what the derivative of any function means. A hint I can give you is that derivatives have to do with 'change'.