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).