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 :
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?