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AP Calculus AB 3.3 Differentiating Inverse Functions Question Bank

Practise inverse-function derivative questions by relating a function and its inverse and evaluating derivatives at corresponding points.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • use inverse-function relationships to connect corresponding input and output points
  • calculate derivatives of inverse functions from the original derivative

FUN-3.E—Calculate derivatives of inverse and inverse trigonometric functions question 1

[Maximum number: 1]

Questions 9 and 10. Use the following table, which shows the values of differentiable functions f\boldsymbol{f} and g\boldsymbol{g}.

Table for Question FUN-3.E—Calculate derivatives of inverse and inverse trigonometric functions question 1 — AP Calculus AB

If H(x)=f−1(x)H(x)=f^{-1}(x), then H′(3)H^{\prime}(3) equals

A

−116-\frac{1}{16}

B

−18-\frac{1}{8}

C

12\frac{1}{2}

D

1

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