AP Calculus AB 5.9 Connecting Function and Derivative Graphs Question Bank

Practise derivative-graph questions by linking sign, zeros, extrema and concavity across a function and its first and second derivatives.

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

[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. $M^{\prime}(t)$
III. $M^{\prime \prime}(t)$

I only

I and II only

I and III only

I, II, and III

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FUN-4.A—Justify conclusions about the behavior of a function based on the behavior of its derivatives—Topic 5.9 question 1