I have to prove the following:

Suppose that functionsfandgare continuous at and f(c) > g(c). Prove there exists > 0 such that for all with , we have f(x) > g(x).

I really have no idea. any help on this would be great thanks!

Printable View

- Oct 22nd 2009, 10:31 PMbinkypooNeed help on this proof
I have to prove the following:

Suppose that functions*f*and*g*are continuous at and f(c) > g(c). Prove there exists > 0 such that for all with , we have f(x) > g(x).

I really have no idea. any help on this would be great thanks! - Oct 22nd 2009, 11:53 PMel_manco
Hello

First you can proof this result.

If is a continuous function in then and , then there exists such that implies .

This follows inmediately from continuous definition; taking there exists such that implies:

Then, for your exercise, apply this result to the funcion . Note that the difference of continuous function is continuous.

Best regards. - Oct 25th 2009, 08:18 PMbinkypoo
[quote=el_manco;389581]taking

do you mean ?? - Oct 25th 2009, 11:40 PMel_manco