Sketch the graph of the function satisfying the following conditions on domain -10 < x < 10
How to graph (using given derivative and intervals)-calculus-rough-graphing-derivative.png
So this is how my teacher showed me what it looks like when you use the information from the table.

So if I were to go through the simple steps to the complex ones, would it be best to go like this?
1. Put all the points given onto the graph (Which would be the single points + f(x) which would be y)
2. Locate the asymptotes (I believed its the point with no f(x), which would be -6, -2, 2, and 6)
3. Try to draw the lines (whether its increasing, decreasing, or concave down)
-This is the one I had a hard time with. But when I went through the table, it decreases, concave down, increases, then it concaves down again? then decreases.) I was confused for the 4th one, because it looks like it increases, but it says concave down.

Also I'm not really sure how the f'(x) and f''(x) play into this table, because I'm mainly using the point/interval and f(x) in this, but not the derivative and second derivative.

So can someone kind of explain to me how to graph points with derivates and understand how to graph the concavity and increasing/decreasing?
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Another example I had was:
How to graph (using given derivative and intervals)-calculus-rough-graphing-derivative-2.png
Though, I did this one wrong... It didn't have like 'increasing, dereasing, or concave down.' I tried my best doing it, but I only got the last one right (the last curve up)

So if someone could explain that, thanks