# Math Help - cost function.

1. ## cost function.

For the given cost function
C(x)=52900+200x+x2 find:
a) The cost at the production level 1000 = $1252900 b) The average cost at the production level 1000 =$1252.9
c) The marginal cost at the production level 1000 = $2201 d) The production level that will minimize the average cost? e) The minimal average cost? I know you have to divide c(x) by x units, then take the derivative... but it's just not working out for me. 2. Originally Posted by B-lap For the given cost function C(x)=52900+200x+x2 find: a) The cost at the production level 1000 =$1252900
b) The average cost at the production level 1000 = $1252.9 c) The marginal cost at the production level 1000 =$2201

d) The production level that will minimize the average cost?
e) The minimal average cost?

I know you have to divide c(x) by x units, then take the derivative... but it's just not working out for me.
$A(x) = \frac{52900+200x+x^2}{x}=\frac{52900}{x}+200+x$

$A'(x) = \frac{-52900}{x^2} + 1$

Find the critical number by setting it equal to zero, since it cannot be undefined; well, it can, but you get x=0 which makes no sense.

$x^2 = 52900$

so x=230

You may want to justify that it's a min (and not a max!) using one of the derivative tests.

The attached summary I give out to my students might help. Good luck!!