Answer:
Consider
Since
modulus function is everywhere continuous and sum of two continuous function is
also continuous.
Differentiability
of f(x)
Graph
of f(x) shows, that f(x) is every where derivable except possible at x = 0 and
x = 1
At x = 0
L.H.D. =
R.H.D.
Since L.H.D. R.H.D.
f(x) is not
derivable at x = 0.
At x = 1
L.H.D. =
R.H.D.
Since L.H.D.
is not
derivable at x = 1 also.
Hence f(x) is
continuous everywhere but not derivable at exactly two points. Hence the result.
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