How do I find the intervals when the graph below is concave up and when it's concave down as well as its inflection coordinate points just by looking at the graph?
I'm able to eyeball it here, but I'm confused with a few parts. I'm pretty sure it concaves up in $(0, 2)\cup(5, \infty)$. I'm not sure if the region around $x=4$ should have its concavity considered because the derivative is not defined at this point. Then I suspect it concaves down in $(2, 3.5)$. Again, I'm not sure if the point after $x=4$ but just before $x=5$ should be considered an interval where it concaves down, but I doubt it.
Then I think the inflection coordinates are $(1, 4), (3, 6), (5, 5)$