Bonus Question involving Continuity?

**Solid8Snake** · February 17th 2010, 03:54 PM

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.

Thx in advance!

**Drexel28** · February 17th 2010, 07:48 PM

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.

Thx in advance!

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.

**Solid8Snake** · February 17th 2010, 07:57 PM

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

thanks.

**vince** · February 17th 2010, 07:59 PM

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.

Thx in advance!

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

**Drexel28** · February 17th 2010, 07:59 PM

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.

**Drexel28** · February 17th 2010, 08:02 PM

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

What a stupid thing to say.

**Solid8Snake** · February 17th 2010, 08:03 PM

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.

**Drexel28** · February 17th 2010, 08:04 PM

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?

**Solid8Snake** · February 17th 2010, 08:05 PM

whether there is a root within a given interval

**Drexel28** · February 17th 2010, 08:06 PM

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.

**Solid8Snake** · February 17th 2010, 08:09 PM

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

**Solid8Snake** · February 17th 2010, 08:10 PM

so in other words would this be sort of what we are getting at
0<c<1?

**Drexel28** · February 17th 2010, 08:11 PM

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 $h(0)>0,h(1)<0$

**Solid8Snake** · February 17th 2010, 08:13 PM

I think I get it now.

Thanks for the help!

**vince** · February 18th 2010, 08:17 AM

Originally Posted by Drexel28

What a stupid thing to say.

easy for you to say

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

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