So here is what I understand:
- If $f(x)$ is increasing/decreasing, then its derivative $f'(x)$ is positive/negative
- If $f(x)$ is increasing/decreasing, then the derivative of $f'(x)$ (which is $f''(x)$) is concave up/concave down
So my question is: if a graph has a vertical asymptote, the derivative must also have a vertical asymptote, too, right? Does it also work vice versa? I feel like there is a trick to it, but I'm not sure.
I have a graph from GeoGebra here. The dotted line is the derivative.