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Math Help - Continuous function ?

  1. #1
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    Continuous function ?

    I have function f(x) which is continuous and nonnegative. Is it possible to show (to prove) that: max f(x)< f(x_0) ( where max f(x) is calculated over the interval |x-x_0|> delta ) implies |x-x_0|< delta ? Thanks in advance.
    Last edited by Zhanna Andrushchenko; November 17th 2008 at 03:18 AM. Reason: unclear writing
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  2. #2
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    Quote Originally Posted by Zhanna Andrushchenko View Post
    I have function f(x) which is continuous and nonnegative. Is it possible to show (to prove) that: max f(x)< f(x_0) ( where max f(x) is calculated over the interval |x-x_0|> delta ) implies |x-x_0|< delta ? Thanks in advance.
    No. If f is the zero function on \mathbb{R} then it is not possible to have \max_{|x-x_0|<\delta} f(x) < f(x_0).
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