Question

is every continuous function differentiable?

Answer 1

Nope, example is this function
y=x, x>0
y=-x, x<=0

it is not differentiable at x=0

Answer 2

it's still differentiable at any x beside x=0, is there a function that is continuous but differentiable nowhere?

Answer 3

I can't think of any function right now but I guess it can be possible.

Answer 4

"is there a function that is continuous but differentiable nowhere"
this is a very complicated subject in math:
the study of functions that are every continuous and nowhere differentiable.
I think there is an example on wikipedia, but this is an advanced idea

Answer 5

ah, here's one that I have never used
the Weierstrass function
http://en.wikipedia.org/wiki/Weierstrass_function
continuous everywhere; differentiable nowhere

Answer 6

Thanks @TuringTest

Answer 7

very welcome
:)

Answer 8

I found this a while back: this is a nice masters thesis on the subject....

http://epubl.luth.se/1402-1617/2003/320/LTU-EX-03320-SE.pdf

Answer 9

@Zarkon This is actually opposite of what he asked. But still interesting topic.

Answer 10

I wish there was something other than best answer like good answer, you deserve one @Zarkon.

Answer 11

jinchuriki3005 wrote...
'is there a function that is continuous but differentiable nowhere?'

Answer 12

I could see the confusion..based on the title of the thesis...

'Continuous nowhere differentiable functions'


it is really Continuous ...but...nowhere differentiable functions

Answer 13

Sorry my bad I read the title this way "continuous nowhere, differentiable function"

Answer 14

Does such a thing exist?

Answer 15

let me say that again...lol

if a function is not continuous then it is not differentabel

Answer 16

diff->continuity

not continuous->not diff

Answer 17

It comes from my imagination and not my math.
we do plot a function for things which are happening in real life and then we find the best line/equation fits the real data we collected. Now let's say we want to differentiate such a function can we do something that the data that we have recorded become more effective than the extra dots which made an equation out the data that we collect?

Answer 18

Another thing came to my mind is that in some application and even control system in real life they find derivative of error by current error from current error and they don't divide it by time. So if you get a close look at the output graph it is made of a lot of straight line in equivalent interval.

Answer 19

thank you, L!!!