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Math Help - [SOLVED] Urgent

  1. #1
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    [SOLVED] Urgent

    Can anyone help on this problem:
    Suppose
    f is defined on (−∞,) and |f(x) f(y)| ≤ K|xy|^α
    for all x, y E(−∞,) and some constants K and α> 0 .
    Show that
    f is continuous on (−∞,) .
    If α
    > 1 , show that f '(x) = 0 for all x E(−∞,)
    Thank you.

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  2. #2
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    If \varepsilon  > 0 define \delta  = \left( {\frac{\varepsilon }{K}} \right)^\frac {1}{a} .
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  3. #3
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    is that only to show is continuous?
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  4. #4
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    \left| {f(x) - f(y)} \right| \le K\left| {x - y} \right|^a  \Rightarrow \quad \left| {\frac{{f(x) - f(y)}}{{x - y}} - 0} \right| \le K\left| {x - y} \right|^{a - 1}
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