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

1 Answer
Apr 30, 2015

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#