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

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Answer 1 · 2015-04-30T15:03:43

A function is non-differentiable at any point at which

a) it is discontinuous,

b) it has a corner point or a cusp

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

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

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 $lim_(xrarra^+) abs(f'(x)) =oo$