marginal cost

[jbrown43]

i have a problem where a certain producer determines that his cost function is c(x)=9000 +3.25x 42x^1/3 determine the cost of producing 1200 units i know that i have to take the derivitive to get this answer i am having a problem with the cube root

1/3*42x^-2/3 +3.25 is what i think derivitive starts as which is 14x^-2/3 +3.25 which is 1/14x^2/3 + 3.25 i believe you would replace x with 1200 and multiply out i do not come up with book answer i come up 3.25009 am i doing this correct?

 

[mmm4444bot]

c(x)=9000 + 3.25x + 42x^(1/3)

i think derivitive starts as … 14x^(-2/3) + 3.25 ← Yes

which is 1/14x^(2/3) + 3.25 ← No

The negative exponent in the derivative applies only to its base x. It does not apply to the coefficient 14.

c`(x) = 14x^(-2/3) + 3.25

If you would like to express c`(x) without a negative exponent, write c`(x) = 14/[x^(2/3)] + 3.25

 

[jbrown43]

Thanks

Thank you for your input helped to work out correctly