Question

How do you find the non differentiable points for a function?

Answer 1

A function is non-differentiable at any point at which

a) it is discontinuous,

b) it has a corner point or a cusp

`color(white)"sssss"` This happens at `a` if

`color(white)"sssss"` `lim_(hrarr0^-) (f(a+h)-f(a))/h != lim_(hrarr0^+) (f(a+h)-f(a))/h`

c) It has a vertical tangent line

`color(white)"sssss"` This happens at `a` if

`color(white)"sssss"` `lim_(xrarra^-) abs(f'(x)) =oo` or `lim_(xrarra^+) abs(f'(x)) =oo`