3. Differentiation(COLON) Composite, Implicit, and Inverse Functions

Differentiating Inverse Functions — Quiz

Test your understanding of differentiating inverse functions with 5 practice questions.

Practice Questions

Question 1

If $f$ and $f^{-1}$ are inverse functions and $f(2)=5$ with $f'(2)=4$, what is $(f^{-1})'(5)$?

Question 2

If $f(x)=x^3+1$, what is $(f^{-1})'(9)$?

Question 3

Which formula gives the derivative of an inverse function in terms of $f$ and $f^{-1}$?

Question 4

Suppose $f(3)=7$ and $f'(3)=0$. What can be said about $(f^{-1})'(7)$?

Question 5

If $f$ is differentiable and one-to-one, and $f^{-1}(4)=1$, which statement is correct?