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Finding the derivative of an unknowable inverse function

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data

    The function f(x) has an inverse function, g(x). Find g'(5).

    2. Relevant equations

    [itex]f(x) = x^5 + 2x^2 + 2x[/itex]


    3. The attempt at a solution

    I don't see how I can possibly find the inverse of this function. So I opted to use the derivative rule for inverses.

    [itex] f'(x) = 5x^4 + 4x + 2[/itex]


    [itex] 5 = x^5 + 2x^2 + 2x[/itex]


    This doesn't help me either. I need to solve for x in the second equation and substitute that x in the derivative. In essence, I can't find x of f(x), and without that I can't find the value of f'(x), which is the reciprocal of g'(x).

    Any help would be appreciated!
     
    Last edited: Sep 27, 2012
  2. jcsd
  3. Sep 27, 2012 #2

    LCKurtz

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    Try a few simple values of x, you will quickly find an x where f(x)=5.
     
  4. Sep 27, 2012 #3
    Oh wow. x=1. That was very foolish of me! Thank you for your time man.
     
  5. Sep 27, 2012 #4
    The answer is g'(5)=1/11 . If anyone is curious.
     
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