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 is concave up in a region where the second derivative (the rate of change of the slope of the graph) is positive. Looking at the graph, we can see that the second derivative changes from negative to positive at $x = 3$, indicating a point of inflection. Therefore, the graph is concave up in the region from $x = 3$ to $x = 6$.

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

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