Continuous function ?

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• November 17th 2008, 02:39 AM
Zhanna Andrushchenko
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.
• November 17th 2008, 06:09 AM
ThePerfectHacker
Quote:

Originally Posted by Zhanna Andrushchenko
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 $\max_{|x-x_0|<\delta} f(x) < f(x_0)$.