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

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The discussion focuses on identifying functions that are continuous everywhere but not differentiable at any point. The Weierstrass function is highlighted as a prime example due to its erratic slope changes. Other functions mentioned include f(x) = sin(π/x) and f(x) = |x|, with the latter having a specific issue at x=0. The conversation also touches on the Dirichlet function, which is discontinuous everywhere, and f(x) = √[3]{x}, which is not differentiable at x=0. The thread concludes with a clarification about the original intent to find functions that are continuous yet not differentiable on any interval.
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.
 


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

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