1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The differenation of abs(x)

  1. Aug 27, 2013 #1
    Hello;

    I want to know why |x| is not differentiable at x=0.

    Thanks
     
  2. jcsd
  3. Aug 27, 2013 #2

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    The limits from the left and from the right are not equal.
     
  4. Aug 27, 2013 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Just look at the graph of |x|. Does it have a unique tangent at x=0?
     
  5. Aug 27, 2013 #4
    .. What is this..

    Aaah, that's a physicist's answer!
     
  6. Aug 27, 2013 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Blast those physicists! (Especially here where that probably the best answer.)
     
  7. Aug 27, 2013 #6
    Compare [tex] lim_{h \to 0^{+}} \frac{|x+h|-|x|}{h} [/tex] and [tex] lim_{h \to 0^{-}} \frac{|x+h|-|x|}{h} [/tex]
     
  8. Aug 27, 2013 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    More "mathematical": the subgradient is not a singleton at x = 0.
     
  9. Aug 27, 2013 #8

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    I should not have said that; it is incorrect.

    Actually, the change in tangent line makes an abrupt, not continuous change at x=0. The lack of a continuous change is the reason why the absolute value of x is not differentiable there.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: The differenation of abs(x)
  1. Abs(Cos(x)) Integral (Replies: 16)

Loading...