Calculus/Economics Question

[mylife]

I've been wasting a lot of time lately and completely put off my online survey of calculus class. I just opened the book for this test 4 hrs ago and the test is in an hour.

Regarding finding the derivative of a function, I know the basic rules and can apply them, but can't see the method behind this problem.

C(x) = .0001x^3 - .08x^2 + 40x + 5000

a. Find the average cost function C bar. (bar=average/mean)
b. Find the marginal revenue cost function C bar of x.

a. C bar of x = .0001x^2 - .08x + 5000/x

b. = .0002x .08 - 5000/x^2

I used the power rule to differentiate the first 2 terms but I don't understand how the part in bold came about. ie how did they go from 5000/x in part a. to 5000/x^2 in part b.

 

[pintoca]

I've been wasting a lot of time lately and completely put off my online survey of calculus class. I just opened the book for this test 4 hrs ago and the test is in an hour.

Regarding finding the derivative of a function, I know the basic rules and can apply them, but can't see the method behind this problem.

C(x) = .0001x^3 - .08x^2 + 40x + 5000

a. Find the average cost function C bar. (bar=average/mean)
b. Find the marginal revenue cost function C bar of x.

a. C bar of x = .0001x^2 - .08x + 5000/x

b. = .0002x .08 - 5000/x^2

I used the power rule to differentiate the first 2 terms but I don't understand how the part in bold came about. ie how did they go from 5000/x in part a. to 5000/x^2 in part b.

Las time I did this was back in 95... nevertheless, I think you got the first part wrong.

The derivative of an x^n expression is not nx^(n-1)

If that is the case, then the first part is indeed wrong.

Again, off the top of my head

 

[mylife]

nah i'm positive the 1st part is right.

straight from the book: The Power Rule = d/dx (x^n) = nx^n-1

thanks though

 

[pintoca]

nah i'm positive the 1st part is right.

straight from the book: The Power Rule = d/dx (x^n) = nx^n-1

thanks though

that is what I wrote... lol

 

[redguru]

d/dx C(x) = 3*.0001x^2- 2*.08x + 40 = 0.0003x^2 - 0.16x + 40

The derivative of a constant is zero.

 

[mylife]

Las time I did this was back in 95... nevertheless, I think you got the first part wrong.

The derivative of an x^n expression is not nx^(n-1)

If that is the case, then the first part is indeed wrong.

Again, off the top of my head

i'm so confused, explain the "not" part to me if you can. or was that just a typo?

 

[pintoca]

i'm so confused, explain the "not" part to me if you can. or was that just a typo?

the typo was I that I forgot to include a ? at the end. It was a question in the negative form

 

[mylife]

ok, now i gotcha.

the first part (a) asks for the average cost function, so i wasn't looking for a derivative. i came to that expression by dividing everything by x.

damn this sucks, i gotta quit fucking around on the internet all the time until i'm outta school and have a real job.

 

[redguru]

Then think of the last term as 5000*x^(-1) The derivative of it would be
-5000x^(-2)

 

[mylife]

ahhh, i see i see

thanks for the help