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!

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- Feb 17th 2010, 03:54 PMSolid8SnakeBonus 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.

Thx in advance! - Feb 17th 2010, 07:48 PMDrexel28
- Feb 17th 2010, 07:57 PMSolid8Snake
I am not quite sure what you mean by what you wrote. Can you please explain in more depth.

thanks. - Feb 17th 2010, 07:59 PMvince
- Feb 17th 2010, 07:59 PMDrexel28
Think about it this way, $\displaystyle h(x)=f(x)-x$ h(0)=f(0)0\geqlsant 0-0=0[/tex] if it's zero we're done. Otherwise it's greater than zero. Similarly $\displaystyle h(1)=f(1)-1\leqslant 1-1=0$. If it's equal zero zero we're done. Otherwise it's less than zero.

- Feb 17th 2010, 08:02 PMDrexel28
- Feb 17th 2010, 08:03 PMSolid8Snake
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, 08:04 PMDrexel28
- Feb 17th 2010, 08:05 PMSolid8Snake
whether there is a root within a given interval

- Feb 17th 2010, 08:06 PMDrexel28
- Feb 17th 2010, 08:09 PMSolid8Snake
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, 08:10 PMSolid8Snake
so in other words would this be sort of what we are getting at

0<c<1? - Feb 17th 2010, 08:11 PMDrexel28
- Feb 17th 2010, 08:13 PMSolid8Snake
I think I get it now.

Thanks for the help! - Feb 18th 2010, 08:17 AMvince