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Mathematics
Problem
If
f
(
x
)
=
{
∣
x
−
1
∣
(
[
x
]
−
x
)
,
x
≠
1
0
,
x
=
1
f(x) = \begin{cases} |x-1|([x]-x), & x \neq 1 \\ 0, & x = 1 \end{cases}
f
(
x
)
=
{
∣
x
−
1∣
([
x
]
−
x
)
,
0
,
x
=
1
x
=
1
Test the differentiability at
x
=
1
x = 1
x
=
1
, where
[
.
]
[. ]
[
.
]
denotes the greatest integer function. Check the differentiability at
x
=
1
x = 1
x
=
1
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