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CTK Exchange
Cibel (Guest)
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Mar-12-01, 01:42 PM (EST) |
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"Analysis Problem"
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There is something about analysis that i dun quite understand.
If f is a continuous function f:R-->R. If f is a local extreme for each
x in R,then f(x)=c. R stand for real number.
To prove this, I try to prove by contradiction and I let f(x_1)=y_1 and
f(x_2)=y_2.
y_1<y_2. If we can show that we can find a interval I in such
that the function is strictly increasing in the interval. But how can I
show this?
To be more precise, what I want to show is:
If f is continusous and if f(x_1)=y_1 and f(x_2)=y_2.
y_1<y_2,x_1<x_2. Then there exist an interval within in which
f is strictly increasing in the interval. |
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alexb
Charter Member
672 posts |
Mar-12-01, 11:59 PM (EST) |
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1. "RE: Analysis Problem"
In response to message #0
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>To be more precise, what I
>want to show is:
>If f is continusous and if
>f(x_1)=y_1 and f(x_2)=y_2.
>y_1<y_2,x_1<x_2. Then there exist an interval
>within in which
>f is strictly increasing in the
>interval. This is not necessarily true. For an example, check the Cantor function: /do_you_know/cantor.shtml |
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