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- May 14th 2008, 05:27 PMszpengchaointermediate value theorem
- May 14th 2008, 05:53 PMarbolis
- May 14th 2008, 05:55 PMszpengchaooh..
i m actually not meaning the first part...

- May 14th 2008, 06:04 PMarbolis
Ok. Next time be more precise then (Wink). Take a look at Mean value theorem - Wikipedia, the free encyclopedia. You must prove this theorem... called the mean value theorem. (or something very close to it).

- May 14th 2008, 06:10 PMszpengchaodotdot
is there any connection between mean value theorem and the thing we asked to prove ?

i mean the f(b') - f(a') / ... = k - May 14th 2008, 06:19 PMarbolisQuote:

is there any connection between mean value theorem and the thing we asked to prove ?

- May 14th 2008, 07:38 PMszpengchaocant see
i still cant see any obvious connection...

anyone who can do it for me please? - May 14th 2008, 07:42 PMszpengchaobe careful
be careful. hav u seen that f'(a) < k < f'(b)

that is f', not f - May 14th 2008, 08:30 PMThePerfectHacker
The intermediate value theorem for derivatives states that if is a differenciable function then has the intermediate value property on , an open interval. Meaning if with and lies (strictly) between and there exists so that .

Without lose of generality we will assume that . Now define the function as . Since is continous on it assumes a minimum value. We will now show that__does not__take a minimum value at . Note that . But since it follows that for sufficiently close to . Thus, there exists so that , which is means , in particular is not a minimum for . Using a similar argument we can show is not a minimum for . Thus, has a minimum on and so there is a point so that .