Minimum Average Cost

[Linty Fresh]

The cost of producing x units of a product is given by:

C(x)=600+100x-100*ln x

Find the minimal average cost.



OK, so average cost should be
Cavg(x)=600/x + (100 - 100*ln x)/x

Taking the derivative of that:
Cavg'(x)=-600/x^2 + 100/x^3

Set the above to 0, multiply both sides by x^3, and you get:
-600x + 100 = 0
x=6

Which wasn't even close by the answer book. I'm thinking I might have messed up taking the derivative of 100*ln x / x, but I'm not sure where I went wrong. Can anyone help? Many thanks.

 

[skeeter]

The cost of producing x units of a product is given by:

C(x)=600+100x-100*ln x

Find the minimal average cost.



OK, so average cost should be
Cavg(x)=600/x + (100 - 100*ln x)/x

no ... C_avg(x) = 600/x + 100 - 100ln(x)/x

Taking the derivative of that:

C'_avg(x) = -600/x² - 100[1 - ln(x)]/x² ... quotient rule, remember?

now proceed to minimize