Thread: problem on continuity and differentiability

Let, f(x) = x , if x is rational
= 0 , if x is irrational.

Then at x=0, which one of he followings is true?
(a) both f and are differentiable
(b) neither f nor are differentiable
(c) is continuous but not differentiable
(d) is differentiable but f is not

please help.

Originally Posted by Sambit

Let, f(x) = x , if x is rational
= 0 , if x is irrational.

Then at x=0, which one of he followings is true?
(a) both f and are differentiable
(b) neither f nor are differentiable
(c) is continuous but not differentiable
(d) is differentiable but f is not

please help.

This is the well-known Dirichlet function: Math Tutor - Functions - Theory - Elementary Functions

ya, but what about ?

Modification 2.

Originally Posted by Sambit

ya, but what about ?

I have provided you with a reference. You are now expected to think.

yes i understood.