I just learn one theorem which says If "$f^{'}$ exists and is monotonic on an open interval (a,b),then $f^{'}$ is continuous on (a,b)."I got the proof but now I am looking for one example in which if I relaxe the hypothesis of monotonic-ness then resulting $f^{'}$ is not continuous.I am thinking but unable to get such example. Thanks.
Asked
Active
Viewed 33 times
0
-
Maybe drop the quotes around theorem statement, as unnecessary... – coffeemath Jan 08 '19 at 13:21
-
If I remember right, $f(x)=x^2\sin{1/x}$ has a discontinuous derivative at $x=0$ – saulspatz Jan 08 '19 at 13:24
-
2There are lots of examples of differentiable functions with discontinuous derivatives. Just search Google. – Ben W Jan 08 '19 at 13:25