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I need an example of a function.

  1. Dec 10, 2014 #1
    • Member warned about not using the homework template
    Give an example of a function f:R2-->R , continuous in (0,0), with partial derivatives in (0,0), but not differentiable in (0,0).

    I was thinking in something like f(x,y)=IxyI
     
  2. jcsd
  3. Dec 10, 2014 #2

    jedishrfu

    Staff: Mentor

    What is the definition of continuous function at a point like (0, 0) ?
     
  4. Dec 10, 2014 #3
    limit as (x,y)->(0,0) of If(x,y)-f(0,0)I=0
     
  5. Dec 10, 2014 #4
    I know what this properties mean, I just can't think of a function with partial derivatives in (0,0) but not differentiable in that point.
     
  6. Dec 10, 2014 #5
    Actually, I think that the function f (x , y) = x1/3y2/3+y1/3x2/3 works fine, am I right?
     
  7. Dec 10, 2014 #6

    jedishrfu

    Staff: Mentor

    Yeah that seems to work. I plotted it here.

    image.jpg

    image.jpg
     
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