Thread: Derivative of Inverse of a cubic

1. 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!

2. 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?