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Problems
Mathematics
Mathematics
Problem
Let
f
(
x
)
=
3
sin
4
x
+
10
sin
3
x
+
6
sin
2
x
−
3
f(x) = 3\sin^4 x + 10\sin^3 x + 6\sin^2 x - 3
f
(
x
)
=
3
sin
4
x
+
10
sin
3
x
+
6
sin
2
x
−
3
,
x
∈
[
−
π
6
,
π
2
]
x \in \left[-\frac{\pi}{6}, \frac{\pi}{2}\right]
x
∈
[
−
6
π
,
2
π
]
Then,
f
f
f
is : (a) increasing in
(
−
π
6
,
π
2
)
\left(-\frac{\pi}{6}, \frac{\pi}{2}\right)
(
−
6
π
,
2
π
)
(b) decreasing in
(
0
,
π
2
)
\left(0, \frac{\pi}{2}\right)
(
0
,
2
π
)
(c) increasing in
(
−
π
6
,
0
)
\left(-\frac{\pi}{6}, 0\right)
(
−
6
π
,
0
)
(d) decreasing in
(
−
π
6
,
0
)
\left(-\frac{\pi}{6}, 0\right)
(
−
6
π
,
0
)
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