Re: local boundedness of derivative



On Sun, 2 Apr 2006, Dusan wrote:

Consider a function f: (a,b)-->R which has a finite derivative f ' on
(a,b). I wonder if the derivative f ' must be locally bounded
on (a,b), i.e. for each x\in (a,b) there exists a neighbourhood U
of x such that f ' is bounded on U.
Thank you.
Dusan

Try the interval (-1,1) and the "monster" function f:

if x is not 0, f(x) = x^2 * sin(1/x^2)
and f(0)=0.

Cheers, ZVK(Slavek).
.