Question

Can anyone give me an example of a function that is CONTINUOUS but not DIFFERENTIABLE? (other than the absolute function) Thanks!

Answer 1

piecewise functions

Answer 2

but those arent continous tho

Answer 3

How about this: f(x) = (x-1)^{1/3}

It is everywhere continuous, but not differentiable at x = 1

Answer 4

what about this one: http://en.wikipedia.org/wiki/Weierstrass_function

Answer 5

\[\sum_{k=0}^{\infty}a^k\cos(b^k\pi x)\]

\[0<a<1;ab>1;b>1\]

Answer 6

(Yes, the construction of everywhere continuous and nowhere differentiable functions is a famous topic in mathematics, but fairly tricky!)

Answer 7

More examples here: http://math.mit.edu/classes/18.013A/HTML/chapter06/section03.html

Answer 8

Mathematical brownian motion

Answer 9

Zarkon - is that a description of the Weierstrass function?

Answer 10

brownian motion ...no

Answer 11

I have never heard of mathematical brownian motion

Answer 12

We should note that mathematical brownian motion is continuous and not differentiable with probability 1

Answer 13

I just looked it up - very interesting: http://en.wikipedia.org/wiki/Brownian_motion

Answer 14

http://en.wikipedia.org/wiki/Wiener_process

Answer 15

yes - that is mentioned in the article I found as well.

Answer 16

f(x) = x, for x <=1
= x^2 for x >1

is continuous ... and not diffied at x=1

Answer 17

works better maybe at the x=0 junction, but same premise :)

Answer 18

amistre, how come it's not differentiable?

Answer 19

if we choose the:

f(x) = x , x<=0
x^2, x>0

we have a cusp, a sharp, nonsmooth, junction at x=0. slope of the line from the left does not match the slope of the line from the right and therefore has no definiable slope for the point at x=0. For the same reason that |x| is not differentiable at x=0 ...

Answer 20

in other words;

the slope from the left is 1 ; the slope from the right is 0

Answer 21

oh okayyyy thanks