Let be a function defined as

,x>=0

, x<0.

What can be said about its differentiability? Is is differentiable at 0? If yes, how many times?

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- Feb 20th 2011, 07:34 AMSambitdifferentiability
Let be a function defined as

,x>=0

, x<0.

What can be said about its differentiability? Is is differentiable at 0? If yes, how many times? - Feb 20th 2011, 08:09 AMFernandoRevilla
Verify so , :

Now, you can study the existence or not of .

Fernando Revilla - Feb 20th 2011, 05:54 PMSambit
I am getting ,x>=0

,x<0

which is differentiable.

Differentiating, , x>=0

,x<0

This is also continuous and differentiable at 0, and so on. So I think it is correct that the function is infinitely differentiable. Am I right? - Feb 20th 2011, 11:33 PMFernandoRevilla

No, prove that:

so, does not exist.

Fernando Revilla - Feb 21st 2011, 03:17 AMSambit
Okay....got it. thank you.