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## Homework Statement

Let f be continuous on R. Is there an open interval on which f is monotone?

## Homework Equations

## The Attempt at a Solution

I think there is such interval for non constant function but I am realy not sure.

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- Thread starter sbashrawi
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- #1

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Let f be continuous on R. Is there an open interval on which f is monotone?

I think there is such interval for non constant function but I am realy not sure.

- #2

HallsofIvy

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- #3

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Continuity doesn't tell you how the fuction approach it's points. If you knew that f '(x) was either negative or postive around some neighbour of your point then you can say if it is monotone or not.

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