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 04:18 AM.
Reason: unclear writing
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 is the zero function on then it is not possible to have .