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Zachary O.

asked • 07/19/18

Calculus question about Derivatives of Inverse Functions

So I have the problem "f(x)=(x^3)-(3x^2)-1,x>=2, find the value of (df^-1)/dx at the point x=-1=f(3)" I keep on getting the answer as 9 but the book says 1/9 and I have no idea why. Could you please explain whats going on?
 
Thank you!!!

Rebecca R.

tutor
Are they asking for the derivative of the inverse of this function? (df-1(x))
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07/19/18

Zachary O.

Yes but at the point x=-1=f(3). It's finding the tangent line to the curve.
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07/20/18

1 Expert Answer

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Zachary O.

Could you explain the third part a little bit more? I don't see why 1 is over the function, but totally understand what the function does.
 
Where does the 1 over f prime at f of 3 come from?
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07/20/18

Mark M.

tutor
Check any Calculus textbook (or Google it) for a derivation of the formula.  Basically, we find the derivative of f(x) and evaluate it at 3 to get 9.  Then, the derivative of the inverse function evaluated at f(3) is the reciprocal of 9 (i.e., 1/9).  
 
Mark M (Bayport, NY)
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07/20/18

Mark M.

tutor
 
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07/21/18

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