I could really use some help. Not really sure how to get started.

Suppose and . Construct nested intervals and such that and . Then show if and .

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- November 2nd 2010, 07:19 PMzebra2147Nested Intervals and IVT
I could really use some help. Not really sure how to get started.

Suppose and . Construct nested intervals and such that and . Then show if and . - November 2nd 2010, 07:25 PMDrexel28
- November 3rd 2010, 05:50 AMzebra2147
is a continuous function on some interval where .

- November 3rd 2010, 08:51 AMDrexel28
- November 14th 2010, 11:05 AMzebra2147
There was a typo to this problem initially. It should read...

Suppose and .

I'm guessing we need to use the Intermediate Value Theorem to show that if there exists then . And then somehow use this to show that and ?? - November 14th 2010, 11:14 AMDrexel28
- November 14th 2010, 03:55 PMzebra2147
Well, my professor never told us but judging by the position of the proof in my notes I think we are trying to help prove the following theorem:

If and are intervals and is continuous, then the range of is an interval.

So is it possible that is an interval?? - November 14th 2010, 04:12 PMDrexel28
- November 14th 2010, 06:22 PMzebra2147
Ok well if we consider could you help me get started?

- November 14th 2010, 06:23 PMDrexel28