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Thread: inverse function derivative

  1. September 3rd 2007, 06:14 PM #1
    runner07
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    inverse function derivative

    how would you do this?

    Suppose that f has an inverse, f(3)=1 and f'(3)=5/3. What is (f^-1)'(1)?
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  2. September 3rd 2007, 06:32 PM #2
    ThePerfectHacker
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    Quote Originally Posted by runner07 View Post
    how would you do this?

    Suppose that f has an inverse, f(3)=1 and f'(3)=5/3. What is (f^-1)'(1)?
    f(f^{-1}(x))=x
    Take derivative of both sides,
    [f^{-1}(x)]'f'(f^{-1}(x))=1
    At x=1 we have,
    [f^{-1}(1)]'f'(f^{-1}(1))=1
    [f^{-1}(1)]'f'(3)=1
    [f^{-1}(1)]'\cdot \frac{5}{3}=1.
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