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AP Calculus AB 5.9 Connecting a Function Its First Derivative and Its Second Derivative Questions

Review AP Calculus AB 5.9 by connecting function, first-derivative, and second-derivative graphs to sign, extrema, and concavity.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • connect zeros and signs of a derivative to extrema of the original function
  • use second-derivative signs to infer concavity and graph shape

Covered syllabus points

FUN-4.A—Justify conclusions about the behavior of a function based on the behavior of its derivatives—Topic 5.9

Question 1

[Maximum number: 1]

The first woman officially timed in a marathon was Violet Piercy of Great Britain in 1926. Her record of 3:40:22 stood until 1963, mostly because of a lack of women competitors. Soon after, times began dropping rapidly, but lately they have been declining at a much slower rate. Let M(t) be the curve that best represents winning marathon times in year t. Which of the following is (are) positive for t>1963 ?

I. M(t)
II. M′(t)M^{\prime}(t)
III. M′′(t)M^{\prime \prime}(t)

A

I only

B

I and II only

C

I and III only

D

I, II, and III

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