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Inverse question

  1. Nov 30, 2009 #1
    given that f(x)=x³+3x+6

    i need to find f^-1'(2)
     
  2. jcsd
  3. Nov 30, 2009 #2
    Hi,
    Derivatives of inverse functions for y=f(x)

    [tex]y=f(x)\Rightarrow f^{-1}(y)=x=f^{-1}(f(x))[/tex] if we take derivatives of both sides dependent to x,

    [tex]f'(x)[(f^{-1})'(f(x))]=1\Rightarrow(f^{-1})'(f(x))=\frac{1}{f'(x)}[/tex].
     
  4. Dec 1, 2009 #3

    HallsofIvy

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    Of course, f'(x) has to be evaluated at the x such that f(x)= 2, so you need to start by solving [itex]x^3+ 3x+ 6= 2[/itex]. Fortunately, that's very easy.
     
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