Assume this function has a value $0$ at $x=0$.
If the right hand derivative of a derivable function is equal to the right hand limit of the derivative function (same for the left), why aren't functions like the one above continuously differentiable?
For a function to be continuous, limits should be finite and equal to value at that particular point.
For this function derivative using first principle yields $0$.
The RHD, LHD is $0$, I think. So why isn't the derivative continuous?
For finding the RHD and LHD, I have seen answers resorting to using known derivatives. My question is: why don't we use the first principle itself? Why do we get different answers then?