Example a function that is continuous at every point but not derivable

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Discussion Overview

The discussion revolves around identifying functions that are continuous at every point but not differentiable. Participants explore various examples and clarify the characteristics of such functions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant requests an example of a function that is continuous everywhere but not derivable.
  • Another participant suggests that the slope of such functions changes erratically.
  • A link to the Weierstrass function is provided as an example of a function that is continuous everywhere but not differentiable.
  • Several participants agree that the Weierstrass function serves as a suitable example.
  • One participant mentions the Dirichlet function but notes that it is discontinuous everywhere, which does not fit the criteria.
  • Another participant proposes functions like f(x) = sin(π/x) and f(x) = |x|, highlighting issues at x=0 regarding differentiability.
  • There is a mention of f(x) = √[3]{x} as an example that is continuous but has a derivative that is problematic at x=0.
  • A participant expresses uncertainty about whether they are addressing functions that are not differentiable on any interval while remaining continuous.

Areas of Agreement / Disagreement

Participants generally agree on the Weierstrass function as a valid example, but there are competing views regarding other functions and their properties, leading to some unresolved aspects of the discussion.

Contextual Notes

Some proposed functions may have ambiguous behavior at specific points, such as x=0, which complicates the discussion of their differentiability.

hadi amiri 4
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can you example a function that is continuous at every point but not derivable
 
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The slope erratically changes.
 


Yes, I also think of the weierstrass function is a perfect example of that.
 


I was thinking the dirichlet function, but that's the one that's discontinuous everywhere.
 


[tex]f(x)= sin (\fraction\pi/x)[/tex]
[tex]f(x) = |x|[/tex]
The problem's ambiguity at x=0.

Any interval on a curve where the derivative would divide by zero. [tex]f(x) = \sqrt[3]{x}[/tex] would do this at x=0.

Edit* I'm sorry if you were looking for functions that are not differentiable on any interval but are continuous.
 
Last edited:

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