Below is a graph of a function $f ( x )$ . Over what region(s) is the graph concave up?
A) at $x = 3$
B) from 0 to 3
C) from 3 to 6
D) None of the above

Question

Below is a graph of a function $f ( x )$ . Over what region(s) is the graph concave up? 
A) at $x = 3$ 
B) from 0 to 3 
C) from 3 to 6 
D) None of the above

Quizplus · Accepted Answer

The graph of a function is concave up when its second derivative is positive. From the graph, we can see that the second derivative changes from negative to positive at x = 3, and remains positive for x values greater than 3 up until around x = 6. This means that the graph is concave up over the region from 3 to 6. Therefore, the correct choice is C.

Below Is a Graph of a Function f(x)f ( x )f(x)

Below Is a Graph of a Function $f ( x )$