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Not possible to find a function g such that g

  1. Jul 31, 2009 #1
    Why is it not possible to find a function g such that g [tex]\in[/tex] C1 at (0,0) and g is not differentiable at (0,0)
     
  2. jcsd
  3. Jul 31, 2009 #2
    Re: Differentiability

    Also given that f(x,y) = x|y| how do I show that f [tex]\notin[/tex] C1 at (0,0)
     
  4. Jul 31, 2009 #3
    Re: Differentiability

    As far as I know, a function is defined to be C1 if it is continuously differentiable, so the question doesn't make sense.
     
  5. Jul 31, 2009 #4
    Re: Differentiability

    Remember the definition of differentiability: all approaches to the point (0,0) must yield the same derivative. Consider approaching the derivative along the x-axis and then the derivative along the y-axis. Are they equal?
     
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