Hello!

I want to know if the following is correct:

I want to prove that the function

is differentiable on all open intervals with

Here is what I did:

I know that the function is linear on the given open intervals and each linear function is differentiable.

To show that the function is not differentiable on I calculated using I'Hospital in the differential quotient :

I'Hospital gives:

On the other hand

Now when k is even then (1) is 1 and (2) -1 and

if k is odd, then (1) is -1 and (2) is even.

Given that fact, it means that the function is not differentiable at

I would do the same calculation with the 2nd endpoint of the given interval.

My question is: Is it correct what I am doing here?

Thanks.

Regards