Non-differentiable functions

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Most functions cannot be differentiated.

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

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.

A unilateral function can have two different results

and

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

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