Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.

Question:

Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.

Solution:

$f(x)=|x|+|x+1|+|x+2|+|x+3|+|x+4|$

The above function is continuous everywhere but not differentiable at x = 0, 1, 2, 3 and 4

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