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Finding the derivative of an unknowable inverse function

  • Thread starter yiyopr
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  • #1
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Homework Statement



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

Homework Equations



[itex]f(x) = x^5 + 2x^2 + 2x[/itex]


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.

[itex] f'(x) = 5x^4 + 4x + 2[/itex]


[itex] 5 = x^5 + 2x^2 + 2x[/itex]


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!
 
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Answers and Replies

  • #2
LCKurtz
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Try a few simple values of x, you will quickly find an x where f(x)=5.
 
  • #3
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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.
 
  • #4
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The answer is g'(5)=1/11 . If anyone is curious.
 

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