Question

Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer ?

Answer 1

Let, the function is,

f( x )={ | x |       ,−∞<x<1 2−x   ,1≤x≤∞

The function is polynomial, so it is continuous everywhere.

Form the above graph of function it can be observed that function is not differentiable at exactly two points x=0 and x=1.