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Problems
Problem
Problem
Statement I
If
f
(
x
)
=
[
x
]
(
sin
x
+
cos
x
−
1
)
f(x) = [x](\sin x + \cos x - 1)
f
(
x
)
=
[
x
]
(
sin
x
+
cos
x
−
1
)
(where
[
⋅
]
[\cdot]
[
⋅
]
denotes the greatest integer function), then
f
′
(
x
)
=
[
x
]
(
cos
x
−
sin
x
)
f'(x) = [x](\cos x - \sin x)
f
′
(
x
)
=
[
x
]
(
cos
x
−
sin
x
)
for any
x
∈
x \in
x
∈
integer.
Statement II
f
′
(
x
)
f'(x)
f
′
(
x
)
does not exist for any
x
∈
x \in
x
∈
integer.
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