Continuous function

  • Thread starter sbashrawi
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  • #1
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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.
 

Answers and Replies

  • #2
HallsofIvy
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You might want to check out the "Weierstrasse function" which is continuous for all x but differentiable nowhere.
 
  • #3
In general, no.

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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