AP Calculus BC 5.8: Function and Derivative Graphs

Practice AP Calculus BC questions on using derivative graphs to determine where a function is increasing and concave up.

[Maximum number: 2]

The graph of the continuous function g, the derivative of the function f, is shown above. The function g is piecewise linear for $-5 \leq x<3$ , and $g(x)=2(x-4)^{2}$ for $3 \leq x \leq 6$ .

For -5<x<6, on what open intervals, if any, is the graph of f both increasing and concave up? Give a reason for your answer.

The graph of f is increasing and concave up on 0<x<1 and 4<x<6 because $f^{\prime}(x)=g(x)>0$ and $f^{\prime}(x)=g(x)$ is increasing on those intervals.

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