# Bonus Question involving Continuity?

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• Feb 17th 2010, 04:54 PM
Solid8Snake
Bonus Question involving Continuity?
I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.

• Feb 17th 2010, 08:48 PM
Drexel28
Quote:

Originally Posted by Solid8Snake
I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.

Let $f:I\mapsto I$ continually ([tex]I=[0,1]). Let $g(x)=f(x)-x$. More obvious now. Consider the function at the endpoints.
• Feb 17th 2010, 08:57 PM
Solid8Snake
I am not quite sure what you mean by what you wrote. Can you please explain in more depth.

thanks.
• Feb 17th 2010, 08:59 PM
vince
Quote:

Originally Posted by Solid8Snake
I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.

lol...if you promise to "thank me" ill do it first thing tomorrow morning. looks str8forward...but i need sleep and ive been getting ripped off with posters not thanking me today (Punch)
• Feb 17th 2010, 08:59 PM
Drexel28
Quote:

Originally Posted by Solid8Snake
I am not quite sure what you mean by what you wrote. Can you please explain in more depth.

thanks.

Think about it this way, $h(x)=f(x)-x$ h(0)=f(0)0\geqlsant 0-0=0[/tex] if it's zero we're done. Otherwise it's greater than zero. Similarly $h(1)=f(1)-1\leqslant 1-1=0$. If it's equal zero zero we're done. Otherwise it's less than zero.
• Feb 17th 2010, 09:02 PM
Drexel28
Quote:

Originally Posted by vince
lol...if you promise to "thank me" ill do it first thing tomorrow morning. looks str8forward...but i need sleep and ive been getting ripped off with posters not thanking me today (Punch)

What a stupid thing to say.
• Feb 17th 2010, 09:03 PM
Solid8Snake
I am very confused, I read what you stated, but like I'm not sure how to apply it since we haven't really used the theorem in depth.
• Feb 17th 2010, 09:04 PM
Drexel28
Quote:

Originally Posted by Solid8Snake
I am very confused, I read what you stated, but like I'm not sure how to apply it since we haven't really used the theorem in depth.

What does the IVT say?
• Feb 17th 2010, 09:05 PM
Solid8Snake
whether there is a root within a given interval
• Feb 17th 2010, 09:06 PM
Drexel28
Quote:

Originally Posted by Solid8Snake
whether there is a root within a given interval

Not really. Look it up, look at what I said and get back to me.
• Feb 17th 2010, 09:09 PM
Solid8Snake
well its stating that a continuous function will take on values within a specific domain, in other words between f(a) and f(b)
• Feb 17th 2010, 09:10 PM
Solid8Snake
so in other words would this be sort of what we are getting at
0<c<1?
• Feb 17th 2010, 09:11 PM
Drexel28
Quote:

Originally Posted by Solid8Snake
well its stating that a continuous function will take on values within a specific domain, in other words between f(a) and f(b)

Ok, so we know that $h(0)\geqslant 0$ and [math\h(1)\leqslant 0[/tex] if either are zero we're done, so assume that neither are. Then $h(0)>0,h(1)<0$
• Feb 17th 2010, 09:13 PM
Solid8Snake
I think I get it now.

Thanks for the help!
• Feb 18th 2010, 09:17 AM
vince
Quote:

Originally Posted by Drexel28
What a stupid thing to say.

easy for you to say (Wait)

... most of the problems are fun for me, so in some sense i should thank them ...lol...cornfest.
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