(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x) = x^{3}+ x. Note that f(2) = 10. Find (f^{-1})`(10).

2. Relevant equations

3. The attempt at a solution

Note that where I have written ` it denotes prime (as in the derivative of).

- Switch the x and y variables. x= y^{3}+ y

- Differentiate implicitly 1= (3y^{2}+ 1)y`

- Solve for y`. y`= 1 / (3y^{2}+ 1). Since y = f^{-1}, then y` = (f^{-1})`

Therefore (f^{-1})` = 1 / (3y^{2}+ 1)

Since f(2) = 10, f^{-1}(10)=2. But my equation is(f^{-1})`,notjust

f^{-1}!! I don't know what to do after this point!

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# Homework Help: Derivatives of Inverse Functions

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