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 $f$ is differentiable and one-to-one, which formula gives the derivative of its inverse at $f(a)$?

Question 2

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

Question 3

Let $f(x)=x^3+1$. What is $(f^{-1})'(2)$?

Question 4

At the point $(3,7)$, the graph of $f$ has tangent slope $-5$. What is the slope of $f^{-1}$ at the corresponding point?

Question 5

A table gives $f(1)=4$ and $f'(1)=\frac{2}{3}$. What is $(f^{-1})'(4)$?