This is the time of year for my annual reading of Lou Talman's nice little three-page paper "A Discontinuous Derivative". You should give it a try. It strains my mind, because I can't figure out how "differentiability implies local linearity" if there are functions running around out there with

Anyway, Lou Talman writes well, with a readable narrative and wit that many math papers lack. He has a page full of papers just about AP Calculus topics.

*f*'(0) defined even though the limit of*f*'(*x*) as x→0 does not exist. So*f*is differentiable at zero, but I can't quite figure out why it is locally linear there. Maybe next year.Anyway, Lou Talman writes well, with a readable narrative and wit that many math papers lack. He has a page full of papers just about AP Calculus topics.

Both the links appear broken to me.

ReplyDeleteI tried to fix them, hopefully they work now.

ReplyDelete