Solve f^-1'(2): Find x for f(x)=x³+3x+6

[jamesbond007]

given that f(x)=x³+3x+6

i need to find f^-1'(2)

 

[coki2000]

given that f(x)=x³+3x+6

i need to find f^-1'(2)

Hi,
Derivatives of inverse functions for y=f(x)

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

$$f'(x)[(f^{-1})'(f(x))]=1\Rightarrow(f^{-1})'(f(x))=\frac{1}{f'(x)}$$.

 

[HallsofIvy]

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