Re: Discontinuous Derivative

Proginoskes wrote:
William Elliot wrote: 
What is an example of a function f:R -> R
with a derivative f' defined on all of R,
that is somewhere or other discontinous?

The integral of |t| from 0 to x; i.e., the function
f(x) = {x^2, if x >= 0; -x^2, if x < 0}.


I think you lost either a 2 or a 1/2 somewhere.

But in any case, surely that has continuous derivative
everywhere.

f'(x)= 2x if x>0, f'(x) = -2x if x<0,
and f'(0)=0 by direction computation, so
f'(x) is just 2|x|, which is continuous.
.