Zachary O.
asked • 07/19/18Calculus 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!!!
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1 Expert Answer
f(x) = x3 - 3x2 - 1 and f(3) = -1
f'(x) = 3x2 - 6x
d/dx [f-1(-1)] = 1 / f'(f(3))
= 1 / f'(-1) = 1/9
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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07/19/18