Graph sketching

Oh god, I'm going to talk about maths for a bit. Ignore me. You might find this interesting if you know what a derivative is and what it means.

This is a curiosity that my friend Anupam came up with. I'm not claiming any credit for noticing it but I thought I'd still share it with y'all.  It only requires very rudimentary calculus, but it produces a result which, the more I think about it, the less intuitive it seems.