Calc 1 question about second derivative graph

So that's the second derivative graph:

http://img84.imageshack.us/img84/1828/ma…

I want to know the critical numbers, values of x where there's an inflection point, local min, local max, where it's increasing and decreasing of the FIRST derivative.. f '

How the hell do I do this? I don't get it. Do I have to "convert" the graph to f ' ? No idea.

Well you should be able to draw a graph shaped like f ' from the graph of f '' . The only information you don't have is the placement of the graph (ie. it could be off by a constant shift +c).

So a few rules of thumb to get you started. f '' is the first derivative of f '. Thus we expect the 0s of f '' to be the local mins and local maxes of f ' (or flat spots). We identify these as points A, C, D, and F. If the value goes from positive to negative, it is a local max. If it goes from neg to pos then it is a local min. If it touches 0 but does not change signs it is a flat spot. So, A is a max, C is a min, D is flat, and F is a max.

The local mins and maxes of f '' will be zeros in f '''. Thus these are the inflection points of f '. So B and E are inflection points.

The graph of f ' is increasing when f '' is pos and decreasing when negative.