AP Calculus BC Fun 4 A Justify Conclusions About the Behavior of a Function Based on the Behavior of Its Derivatives Topic 5 9 Questions

Practice AP Calculus BC questions on combining derivative sign and derivative behavior to identify intervals of increase and concavity.

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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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AP Calculus BC Fun 4 A Justify Conclusions About the Behavior of a Function Based on the Behavior of Its Derivatives Topic 5 9 Questions question 1