Question

dx 6. Give an example of a function which is continuous but not differentiable at two points. (2M)​

Answer 1

Since we know that modulus functions are continuous at every point, So there sum is also continuous at every point. But it is not differentiable at every point.

In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve.

We have the statement which is given to us in the question that: Every continuous function is differentiable. ... Therefore, the limits do not exist and thus the function is not differentiable. But we see that f(x)=|x| is continuous because limx→cf(x)=limx→c|x|=f(c) exists for all the possible values of c.