A function and its graph are given. Use the second derivative to determine intervals on which the function is concave up. Check these results against the graph shown.
D) or

Question

A function and its graph are given. Use the second derivative to determine intervals on which the function is concave up. Check these results against the graph shown. ​  ​  ​
D) or

Quizplus · Accepted Answer

The second derivative tells us about the concavity of the function.
- If f''(x) > 0, then the function is concave up.
- If f''(x) < 0, then the function is concave down.

From the graph given, we can see that the function is concave up on the intervals between the local maxima and the inflection point:
- Interval 1: (−1, 1)
- Interval 2: (3, 4)

Looking at the choices, only D includes both of these intervals.

A Function and Its Graph Are Given