Is there an open interval on which f is monotone? explain why?

Question

let f be continuous on R. Is there an open interval on which f is monotone? explain why?

No, its not. One of my colleague asked me.but I got it. Thank you — user139865, Apr 02 '14 at 17:38
@user139865 It's the same thing or at the very least, it is equivalent. — Git Gud, Apr 02 '14 at 18:03

score 3 · Answer 1 · answered Apr 02 '14 at 17:18

3

No. Look up any example of a continuous nowhere differentiable function.

answered Apr 02 '14 at 17:18

Umberto P.

does this example works also if we are defining differentiability as the common finite value of the upper and lower derivatives? – Intuition Oct 29 '19 at 08:47
How is that different from any other definition? – Umberto P. Oct 29 '19 at 13:41
it is looking more complicated at least – Intuition Oct 29 '19 at 13:42

1 Answers1