# Thread: Identifying inflection points of an f" graph

1. ## Identifying inflection points of an f" graph

The graph of the second derivative f '' of a function f is shown. State the x-coordinates of the inflection points of f.

x= (smaller value)
x= (larger value)

On f(x) graphs, it is where the slope changes from + to -(0, point at which not increasing or decreasing). On f'(x) graphs, it's where there are horizontal tangents (slope =0). So for f"(x) it should be wherever the function crosses the x -axis? Which would be x=1, and x=8?

2. Well, on f(x) P.I.'s are where the graph changes concavity , on the graph of f'(x) is where the slope is zero e.i. local max. or min. . And in the graph of f''(x) (you are right) it is the x-intercepts. So in the graph of f''(x) it seems to be (1,0) , (6,0), (8,0).

3. Originally Posted by hazecraze
The graph of the second derivative f '' of a function f is shown. State the x-coordinates of the inflection points of f.

x= (smaller value)
x= (larger value)

On f(x) graphs, it is where the slope changes from + to -(0, point at which not increasing or decreasing). On f'(x) graphs, it's where there are horizontal tangents (slope =0). So for f"(x) it should be wherever the function crosses the x -axis? Which would be x=1, and x=8?
yes ... where f''(x) changes sign.