Math  /  Calculus

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The derivative of the twice-differentiable function ff is shown below on the domain (9,9)(-9,9). The graph of ff^{\prime} has points of inflection at x=3,x=1x=-3, x=1, indicated by small green circles. What inferences can be made about the graphs of f,ff, f^{\prime}, and ff^{\prime \prime} on the interval (3,0)(-3,0) ? Choose the best answer for each dropdown.
Answer Attempt 2 out of 2 From the figure given above, it can be seen that the graph of ff^{\prime} on the interval (3,0)(-3,0) is positive increasing \square , and concave dow \square Based on these observations, it can be concluded that: On the interval (3,0)(-3,0), the graph of ff would be increasing and concave dow \vee because ff^{\prime} is positive and increasing On the interval (3,0)(-3,0), the graph of ff^{\prime \prime} would be positive only because ff^{\prime} is increasing

Studdy Solution
Since f f' is increasing on (3,0)(-3, 0), f>0 f'' > 0 on this interval.
Based on the analysis, the conclusions are: - On the interval (3,0)(-3, 0), the graph of f f is increasing and concave up. - On the interval (3,0)(-3, 0), the graph of f f'' is positive.

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