Results 1 to 3 of 3

Math Help - Rate of Change

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    19

    Rate of Change

    A company knows that unit cost C and unit revenue R from the production and sale of x units are related by  C= (R^2/176,000) + 9330. Find the rate of change of revenue per unit when the cost per unit is changing by $12 and the revenue is $4000.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Related rates nearly always depend on the chain rule, so you might want to try filling up this pattern...



    ... where straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x, because we're speaking of rates of change with respect to x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    Here we're given a formula relating two variables, which is the top row...



    So differentiate with respect to the inner function, and the inner function with respect to x...

    Spoiler:


    Clearly, you can now substitute the given values of R and dC/dx then solve for dR/dx.

    __________________________________________
    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,974
    Thanks
    1121
    Quote Originally Posted by akuczma86 View Post
    A company knows that unit cost C and unit revenue R from the production and sale of x units are related by  C= (R^2/176,000) + 9330. Find the rate of change of revenue per unit when the cost per unit is changing by $12 and the revenue is $4000.
    \frac{dC}{dt}= \frac{1}{98,000}R \frac{dR}{dt}.

    You are told that [tex]\frac{dC}{dR}= 12 and R= 4000. You can calculate C from C= \frac{(4000)^2}{176000}+ 9330 and put those numbers into the equation above.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rate of change?
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: December 8th 2011, 03:16 AM
  2. Replies: 3
    Last Post: April 12th 2011, 09:51 AM
  3. rate of change
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 17th 2009, 08:23 AM
  4. rate of change
    Posted in the Calculus Forum
    Replies: 9
    Last Post: May 3rd 2007, 09:39 AM
  5. Rate of change
    Posted in the Statistics Forum
    Replies: 2
    Last Post: April 18th 2007, 07:27 AM

Search Tags


/mathhelpforum @mathhelpforum