Hi

I have this problem I haven been trying to solve for a while:

"Check if the following function is continuous and/or differentiable :"

Code:

/ (x^2-1) /2 , |x|=< 1
f(x) = \ |x| -1 , |x| > 1

So I managed to prove it is continuous for all x by checking the limits as x -> 1 from both directions = 0

and the limit as x -> 0 from both directions = -1/2 (is that necessary?)

from that point it's continuous for all x as a polynomial in either branch.

is that correct so far?

now the problem starts with the derivative check...

I get that the f'(x) = x , |x| < 1

or f'(x) = x/|x| , |x| > 1