# Finding the derivative of an unknowable inverse function

## Homework Statement

The function f(x) has an inverse function, g(x). Find g'(5).

## Homework Equations

$f(x) = x^5 + 2x^2 + 2x$

## The Attempt at a Solution

I don't see how I can possibly find the inverse of this function. So I opted to use the derivative rule for inverses.

$f'(x) = 5x^4 + 4x + 2$

$5 = x^5 + 2x^2 + 2x$

This doesn't help me either. I need to solve for x in the second equation and substitute that x in the derivative. In essence, I can't find x of f(x), and without that I can't find the value of f'(x), which is the reciprocal of g'(x).

Any help would be appreciated!

Last edited:

LCKurtz
Homework Helper
Gold Member
Try a few simple values of x, you will quickly find an x where f(x)=5.

Try a few simple values of x, you will quickly find an x where f(x)=5.

Oh wow. x=1. That was very foolish of me! Thank you for your time man.

The answer is g'(5)=1/11 . If anyone is curious.