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Non-differentiable functions

Most functions cannot be differentiated.

 


Explanation

Differentiable functions are very atypical among continuous functions. In order to be differentiable, a function must meet several conditions.

 


Example 1

The lateral derivatives of the function f (x) = | x | in x = 0 are

This function cannot be differentiated at this point, as the tangent lines from left and from right are not equal.

 


Example 2

A unilateral function can have two different results

and

so that this function is not differentiable in the point x = 0.

 


Additional information

The Polish mathematician Stefan Banach (1892 - 1945) claimed that there are few differentiable functions.


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