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Thread: Derivative of Inverse of a cubic

  1. #1
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    Derivative of Inverse of a cubic

    I have the formula for this problem (the green) but I can't find the inverse easily. Is there a trick that's appropriate for a AP Calc class? Thanks!
    Derivative of Inverse of a cubic-revu_2018-12-04_19-21-51.png
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  2. #2
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    Re: Derivative of Inverse of a cubic

    $f(x) = 2x^3-3x$

    notice that $f(1) = -1 \implies f^{-1}(-1) = 1$


    using your formula, $(f^{-1})'(-1) = \dfrac{1}{f'[f^{-1}(-1)]} = \dfrac{1}{f'(1)}$



    can you finish it up?
    Thanks from lamp23
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