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AP Calculus AB 5.8 Sketching Functions and Derivatives Question Bank

Practise graph-sketching questions by connecting a function with its first and second derivatives, intercepts, extrema and concavity.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • use derivative signs to sketch increasing and decreasing behavior
  • connect extrema and concavity of a function to its derivative graphs

FUN-4.A—Justify conclusions about the behavior of a function based on the behavior of its derivatives—Topic 5.8 question 1

[Maximum number: 1]

Given f′f^{\prime} as graphed, which could be a graph of f ?

Figure for Question FUN-4.A—Justify conclusions about the behavior of a function based on the behavior of its derivatives—Topic 5.8 question 1 — AP Calculus AB
A

I only

B

II only

C

III only

D

I and III only

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