How Graphs are affect by higher order derivatives

[ncbs77]

How does higher order derivatives affect the graph? Mostly just the 3rd, 4th or 5th derivatives. I believe I have found the 3rd one but I'm not sure about it or the others.

 

[gb7nash]

How does higher order derivatives affect the graph?

What does this mean?

The first derivative tells you the slope of the original graph. The second derivative tells you the concavity of the original graph.

 

[ncbs77]

I knew of the first two derivatives but I guess there is higher than the second derivative that can affect the graph. Well maybe not exactly the graph like the first or second derivatives but they do show something like about the graph or something like that.