Question

How and when does a non-differentiability happen?

Answer 1

@ByteMe can u help?

Answer 2

non-differentiability occurs when a function can't be differentiated at a certain point.
Take:
\[\frac{5x}{x-1}\]
As you see, when x = 1, the denominator becomes 0 and is thus undefined.
This means that the function is non-differentiability at x = 1.
Simply put it: when it is impossible to differentiate it.

Answer 3

Of course, non-differentiability occurs when the function is not defined.
But more generally, non-differentiability occurs when the limit does not exist in the difference quotient: \(\large \lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h} \)