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October 13th, 2013, 09:46 PM   #11
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Re: What does this mean: f' does not exist (1e derivative te

Ok thanks Greg, that's a weird function.
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October 14th, 2013, 02:32 AM   #12
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Re: What does this mean: f' does not exist (1e derivative te

I didn't specify the domain of abs(x) because I supposed it is obvious what I mean, the whole R line. I apologize.

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y=abs(x) is not a continuous function.
Contra-intuitive and untrue. The abs(x) function (domain = R) is continuous anywhere. A corner is continuous; everyone who has ever drawn a house knows that you can draw a corner without lifting up your pencil.

Undefined and non-existence are synonymous in this context, at least the asker and me used it interchangeably. So I don't think it would be a grammar issue.

Last edited by skipjack; January 19th, 2016 at 06:09 PM.
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October 14th, 2013, 05:02 AM   #13
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Re: What does this mean: f' does not exist (1e derivative te

ok, thanks for the education.
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October 14th, 2013, 05:33 AM   #14
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Re: What does this mean: f' does not exist (1e derivative te

A graphical explanation of differentiation might suffice to make OP understand : Differentiation of a function f at point x = x0 is the interior angle the tangent at x0 on the curve y = f(x) makes with x-axis -- this is something basic I learned - by myself - before even looking at the formal definition of differentiation.

Now, try to think about the point x = 0 of y = |x| and its neighborhoods. Plot the graph by yourself, to be sure. Now tell me this -- do you see that there are infinitely many tangents drawable at x = 0? If you do, then do you realize that the derivative cannot be found there, since there are infinitely many angles formed by infinitely many tangents intersecting at x-axis? So, can you make a meaning of what "undefined" means?

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Originally Posted by Melody2
y=abs(x) is not a continuous function
I think you meant "kinky". Yes, that is certainly so, abs(x) is kinky, as one would say to every function that is not differentiable everywhere. Furthermore, I would simply say that every function is kinky which isn't infinitely differentiable anywhere -- overkill for some people, I guess.

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Originally Posted by Melody2
A function must be continuous for it to be differentiable at any given point.
Obviously, but the converse is not true, as Gregory showed you -- there are uncountably infinitely many functions constructible that are not differentiable anywhere but continuous everywhere.

Last edited by skipjack; January 19th, 2016 at 06:13 PM.
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