1

I am just confused on the structure of differentiable functions whose derivative is also continuous. How will that continuous function be? What extra restrictions one need to put so as to make a derivative of continuous function continuous? Given an arbitrary continuous function can we be able to say about the continuity of its derivative ? What are the properties of such functions?

MB17
  • 163
  • Given an arbitrary continuous function, it need not be differentiable anywhere, let alone continuously differentiable. see e.g. Weierstrass function –  Jul 12 '19 at 05:41
  • “Continuous differentiable” means continuous and differentiable, which is redundant, since differentiable implies continuous. What you want to say is continuously differentiable, i.e., “differentiable in a continuous way”. – Hans Lundmark Jul 12 '19 at 06:19
  • I mean about the functions that have continuous derivative. – MB17 Jul 12 '19 at 08:21
  • 1
    See cite1 (specific examples with useful graphs shown), cite2 and cite3 (how bad things can get), cite4 (how good things must be), cite5 (discussion of *big* in the sense of Baire category and in the sense of Lebesgue measure, two notions that arise in describing how bad things can be and how good things must be). – Dave L. Renfro Jul 12 '19 at 09:44

0 Answers0