AP Calculus BC 5.9 Graph Relationships Overview

Review graph relationships by translating between a function and its first- and second-derivative graphs, using signs and turning points as evidence.

Covered syllabus points

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

[Maximum number: 2]

The function f is defined on the closed interval [-5, 4]. The graph of f consists of three line segments and is shown in the figure above. Let g be the function defined by $g(x)=\int_{-3}^{x} f(t) d t$ .

On what open intervals contained in -5<x<4 is the graph of g both increasing and concave down? Give a reason for your answer.

$g^{\prime}(x)=f(x)$
The graph of g is increasing and concave down on the intervals -5<x<-3 and 0<x<2 because $g^{\prime}=f$ is positive and decreasing on these intervals.

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Covered syllabus points

5.9 Connecting a Function, Its First Derivative, and Its Second Derivative question 1