Hi, Can someone help me ?

[DotFiller]

Either f a continuous and strictly positive function over an interval [a,b]
Show that : (We have at least α>0);(for any x from [a,b]) f(x)=>α
Either g and h a continuous functions over [a,b]
Such that:
(for any x from [a,b]) g(x)>h(x)

Show that:
(We have at least ω>0);(for any x from [a,b]) g(x)=>h(x)+ω

 

[Steven G]

This is a free math help forum and not a free math homework service. If you want help you really need to read the forum's posting guidelines so you know the requirements to receive help. The main point of the guidelines is that you need to post a clear question and share your attempt at doing the problem--even if you know it is wrong. Seeing your work enables the helpers on this forum see the way you want to solve this problem and of course see if you made any mistakes.

 

[DotFiller]

This is a free math help forum and not a free math homework service. If you want help you really need to read the forum's posting guidelines so you know the requirements to receive help. The main point of the guidelines is that you need to post a clear question and share your attempt at doing the problem--even if you know it is wrong. Seeing your work enables the helpers on this forum see the way you want to solve this problem and of course see if you made any mistakes.

Do you can help me ?

 

[topsquark]

Do you can help me ?

Can you show us what work you've been able to do on this? Even if it is wrong?

We can't see the mistake until we can see your work!

-Dan

 

[pka]

Either f a continuous and strictly positive function over an interval [a,b]
Show that : (We have at least α>0);(for any x from [a,b]) f(x)=>α

To DotFiller: I take that you are not a native English speaker. It took me a great deal of reading to under what your first question means. But I have not a clue about the second. I think the first is about the consequences of the Heine-Borel theorm;
Some undergraduate calculus textbooks call it the Mini-Max theorem: every continuous function on a compact real number set (i.e. a closed and bounded set). has a minimum & a maximum in that set. Now you need to study the link provided above and post what you can.