Continuity And Differentiability

Question

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

Solution

Let function f be defined by
f(x) = |x - 1| + |x - 2| + |x - 3| + |x - 4| + |x - 5|
This function is continuous everywhere.
Also it is differentiable everywhere except at x = 1, 2, 3, 4, 5.
Hence the result.

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Continuity And Differentiability

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

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