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October 13th, 2013, 08:46 PM  #11 
Senior Member Joined: Oct 2013 From: Sydney Australia Posts: 126 Thanks: 0  Re: What does this mean: f' does not exist (1e derivative te
Ok thanks Greg, that's a weird function. 
October 14th, 2013, 01:32 AM  #12  
Senior Member Joined: Feb 2013 Posts: 281 Thanks: 0  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. Quote:
Undefined and nonexistence 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 05:09 PM.  
October 14th, 2013, 04:02 AM  #13 
Senior Member Joined: Oct 2013 From: Sydney Australia Posts: 126 Thanks: 0  Re: What does this mean: f' does not exist (1e derivative te
ok, thanks for the education.

October 14th, 2013, 04:33 AM  #14  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  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 xaxis  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 xaxis? So, can you make a meaning of what "undefined" means? Quote:
Quote:
Last edited by skipjack; January 19th, 2016 at 05:13 PM.  

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