Few days ago I was playing with graphing tool . For some function the graph came out to be like this-
When I zoomed it where it begins,it gave graph like this-
I was curious to know weather function is increasing just after $x=0$ or decreasing. But unfortunately I don’t remember what function I wrote that time. Can someone please help me becuase I keep thinking about this.
Try $x \sin(1/x)$.
For more generality, try
$x^a\sin(1/x^b)$ for different values of $a$ and $b$.