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Infinitely differentiable

  1. Aug 24, 2005 #1
    infinitely differentiable doesn't care if all the higher derivatives are zeroes (like for polynomials), it only has to be defined...correct?
     
  2. jcsd
  3. Aug 24, 2005 #2

    AKG

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    Correct......
     
  4. Aug 24, 2005 #3

    Hurkyl

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    It's okay for them to all be zero as well!

    such as for

    [tex]
    f(x) = \left\{
    \begin{array}{ll}
    0 & x = 0 \\
    e^{-1/x^2} \quad & x \neq 0
    \end{array}
    [/tex]

    at x = 0.
     
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