I am having trouble making sense of how to figure out what a graph looks like just by knowing the critical numbers and the intervals the function is increasing and when it is decreasing. For example I have $(-\infty, -1), (0,1)$ as negative and $(-1,0), (1,+\infty)$ as positive.
I know that the it can only change on critical numbers so that means if I have increase, critical number and then decreasing then I have a graph that is going up and then down and the critical number is a minimum. If I have decrease, critical number and then an increase I have a minimum.
The problem I ma having is determing how to view these. If I start from the left of the function I get concave up (minimums) with decrease, critical number, increase.
If I do the same with an increase, critical number decrease by starting from the right side I get a concave down (max).
How do I know which is correct when working with just this information? It seems to depend entirely on which side I start on.