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I understand that in the graph of f'(x), zeros and local extrema are local extrema and points of inflection, respectively, for f(x). The basic concept of checking direction and rough changes in slope to find concavity also makes sense to me.

However, I'm having a bit of a mental block trying to visualize f(x) from f'(x) when f'(x) goes off inflecting without crossing the x axis.

http://imageshack.us/a/img202/5001/captureipi.png [Broken]

For example, in the above graph I understand what's happening at the first critical point and when h'(x) crosses the x axis, but I don't logically understand what's going on after the second zero. I can easily go through like a robot to find concavity via the second derivative, but I'd like to actually understand the logic behind what's happening here.

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# Sketching graph of f(x) from graph of f'(x)

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