The graph of is shown on the graph above.For which of the stated interval(s) is the function both increasing and concave up?

Question

The graph of  is shown on the graph above.For which of the stated interval(s)is the function  both increasing and concave up?​ ​  ​
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Quizplus · Accepted Answer

A function is increasing and concave up when its first derivative is positive and its second derivative is also positive. From the graph, we can see that the function is increasing on the interval (1, 4) and (6, 7), and it is concave up on the interval (3, 4) and (6, 8). The only interval that satisfies both conditions is (6, 8), which is marked by C on the graph.

The Graph of Is Shown on the Graph Above