Results 1 to 3 of 3

Math Help - Finding the rate of change of an inverse function given certain values

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    64

    Finding the rate of change of an inverse function given certain values

    Hi,

    The problem says:

    For a function f it is given that
    f'(7)= -4 f^-1(7)= -3
    f'(-3)= 12 f^-1(-3)=8

    Find the rate of change of f^-1(x) at x=7.

    I have been trying to solve this problem, but I am getting very confused so I am getting nowhere. I would really appreciate it if anyone could give me a hand. Thanks!

    I know this so far, but I think I haven't got it right...

    f(f^-1(x))=x. Let y=f^-1(x), then f(y)=x.

    So (df/dy)*(dy/dx)=1 --> dy/dx=1/(df/dy) --> dy/dx=1/(f'(-3)) as f^-1(7)=-3. So dy/dx=1/12
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,963
    Thanks
    1631
    You have that exactly right. What makes you think otherwise?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2010
    Posts
    64
    Thanks a lot! I'd asked someone in my class and he said he thought it was wrong...but I'm glad he was wrong. I am kind of new to this so I wasn't sure.

    Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the instantaneous rate of change
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 27th 2011, 05:17 PM
  2. Replies: 1
    Last Post: May 1st 2011, 11:17 AM
  3. Replies: 3
    Last Post: April 12th 2011, 09:51 AM
  4. inverse trig values and finding inverse
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 6th 2009, 12:04 AM
  5. Finding a Rate of Change?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 18th 2009, 06:59 PM

Search Tags


/mathhelpforum @mathhelpforum