1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Monotonically Increasing Functions
Find interval...
Question
Find intervals in which the function given by
f
(
x
)
=
sin
3
x
,
x
∈
[
0
,
π
2
]
is decreasing.
Open in App
Solution
f
(
x
)
=
sin
3
x
f
(
x
)
=
3
cos
3
x
f
(
x
)
=
0
⇒
cos
3
x
=
0
⇒
x
=
π
6
,
π
2
Take
(
0
,
π
6
)
+
(
π
6
,
π
2
)
x
∈
(
0
,
π
6
)
+
x
∈
(
π
6
,
π
2
)
0
≤
3
x
<
π
2
⇒
cos
3
x
<
0
cos
3
x
>
0
when
0
≤
3
x
<
π
2
⇒
f
(
x
)
<
0
⇒
f
(
x
)
>
0
⇒
f
(
x
)
is increasing in
(
0
,
π
6
)
⇒
f
(
x
)
is decreasing in
(
π
6
,
π
2
)
Suggest Corrections
0
Similar questions
Q.
Find intervals in which the function given by
f
(
x
)
=
sin
3
x
,
x
∈
[
0
,
π
2
]
is increasing function
Q.
Find the interval in which the function given by
f
(
x
)
=
sin
3
x
,
x
ϵ
[
0
,
π
2
]
is increasing.
Q.
Find the interval in which
f
(
x
)
=
sin
3
x
−
cos
3
x
,
0
<
x
<
π
is strictly increasing or strictly decreasing.
Q.
Find the intervals in which the function
f
(
x
)
=
sin
4
x
+
cos
4
x
∀
x
∈
[
0
,
π
/
2
]
is increasing and decreasing.
Q.
The following function are decreasing in given interval
f
(
x
)
=
sin
4
x
+
cos
4
x
,
x
∈
(
0
,
π
/
4
)
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Monotonicity
MATHEMATICS
Watch in App
Explore more
Monotonically Increasing Functions
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app