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Mathematics
Mathematics
Problem
Consider
f
(
x
)
=
sin
x
+
cos
x
f(x)=\sin x+\cos x
f
(
x
)
=
sin
x
+
cos
x
on the interval
[
0
,
2
π
]
[0,2\pi]
[
0
,
2
π
]
. On which of the following intervals is
f
f
f
increasing? a)
(
π
4
,
5
π
4
)
(\dfrac{\pi}{4},\dfrac{5\pi}{4})
(
4
π
,
4
5
π
)
b)
(
0
,
3
π
4
)
and
(
7
π
4
,
2
π
)
(0,\dfrac{3\pi}{4})\text{ and }(\dfrac{7\pi}{4},2\pi)
(
0
,
4
3
π
)
and
(
4
7
π
,
2
π
)
c)
(
0
,
π
4
)
and
(
5
π
4
,
2
π
)
(0,\dfrac{\pi}{4})\text{ and }(\dfrac{5\pi}{4},2\pi)
(
0
,
4
π
)
and
(
4
5
π
,
2
π
)
d)
(
0
,
π
4
)
(0,\dfrac{\pi}{4})
(
0
,
4
π
)
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