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Mathematics
Mathematics
Problem
If
f
(
x
)
=
{
[
cos
π
x
]
,
x
≤
1
2
{
x
}
−
1
,
x
>
1
f(x) = \begin{cases} [\cos \pi x], & x \le 1 \\ 2\{x\} - 1, & x > 1 \end{cases}
f
(
x
)
=
{
[
cos
π
x
]
,
2
{
x
}
−
1
,
x
≤
1
x
>
1
, where
[
⋅
]
[\cdot]
[
⋅
]
and
{
⋅
}
\{\cdot\}
{
⋅
}
denote greatest integer and fractional part of
x
x
x
, then a.
f
′
(
1
−
)
=
2
f'(1^-) = 2
f
′
(
1
−
)
=
2
b.
f
′
(
1
+
)
=
2
f'(1^+) = 2
f
′
(
1
+
)
=
2
c.
f
′
(
1
−
)
=
−
2
f'(1^-) = -2
f
′
(
1
−
)
=
−
2
d.
f
′
(
1
+
)
=
0
f'(1^+) = 0
f
′
(
1
+
)
=
0
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