AP Calculus BC Fun 4 A Justify Conclusions About the Behavior of a Function Based on the Behavior of Its Derivatives Topic 5 8 Questions

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

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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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AP Calculus BC Fun 4 A Justify Conclusions About the Behavior of a Function Based on the Behavior of Its Derivatives Topic 5 8 Questions question 1