Continuous but not differentiable...?

Question

It is well known that continuity doesn't imply differentiability. Which means that it is possible to have functions that are continuous everywhere and differentiable nowhere. I know only of one such example, given to us by Weierstrass as the sum as n goes from zero to infinity of (B^n)*Sin((A^n)*pi*x) where A and B can be any numbers that satisfy 01+(3pi/2).

The reason this is continuous because you are simply adding continuous functions but it is not differentiable because it becomes very jaggedy.

The question is, do you know of any other examples where the function is continuous everywhere but differentiable nowhere?

Leah, I am not talking about continuity and differentiability at one single point. I am talking about everywhere.

y=abs(x) is continuous at zero but not differentiable. But everywhere else it IS continuous and differentiable.

I am asking for other examples that ARE continuous everywhere but differentiable NOWHERE!

Smutty, same thing. You are talking about one point. I am talking about all real numbers.

Answer 1

The Blancmange function http://mathworld.wolfram.com/BlancmangeFunction.html

Answer 2

f(x) = - x ^ 2 for x<= 0 and f(x) = x for x >0. f(x) is continuous over the set of real numbers, but not diff on x = 0

Answer 3

i'm questioning a logaritmic function might want to artwork as d/dx(ln (f(x)) = f '(x)/f(x) eg f(x) = ln(x-3) f '(x) = a million/(x-3) f '(x) = a million/(x-3) isn't non-stop at x=3 yet f(x) = ln(x-3) is non-stop at x=3 solid success!