Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is mod x differentiable at all points

  1. Oct 4, 2011 #1
    f(x)= mod x is this function differentiable at all points other than 0.
     
  2. jcsd
  3. Oct 4, 2011 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    What do you mean by f(x) = mod x?
    Usually, mod is used in an expression like "6 mod 4 = 2", and "mod 4" by itself doesn't really mean anything.

    Did you mean "f(x) = |x|", the absolute value of x?
    In that case, the answer is yes: you can easily see this by showing that it is equivalent to x for x > 0 and -x for x < 0. To prove that it is non-differentiable at x = 0, you need to do a little work, but that's still straightforward.
     
  4. Oct 4, 2011 #3
    yes its absolute value of x :)
     
  5. Oct 4, 2011 #4
    Why did you use the term mod for absolute value? I'm not familiar with that application of mod.
     
  6. Oct 4, 2011 #5

    gb7nash

    User Avatar
    Homework Helper

    I think the OP meant modulus, which is another term for absolute value.
     
  7. Oct 4, 2011 #6
    Don't use unapproved abreviations! Haha, i got confused.
     
  8. Oct 5, 2011 #7
    Yes; one way of seeing it is look at |x| as the piecewise function:

    f(x)=x , if x≥0
    f(x)=-x, if x≤0

    Then the function is linear , and if you accept that for n>1, d/dx(xn)=nxn-1, then f is differentiable in (0,∞), and in (-∞,0), and the only possible problem is at x=0.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook