1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Condition for Monotonically Decreasing Function
If fx = x5 ...
Question
If
f
(
x
)
=
x
5
−
20
x
3
+
240
x
, then f(x) is
A
monotonic increasing everywhere
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
monotonic decreasing only in
(
0
,
∞
)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
monotonic decreasing everywhere
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
monotonic increasing only in
(
−
∞
,
0
)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
A
monotonic increasing everywhere
f(n)=
x
5
−
20
x
3
+
240
x
f
(
n
)
=
5
x
4
−
60
x
2
+
240
f
′
(
n
)
=
5
x
4
−
60
x
2
+
240
5
x
2
−
60
x
2
+
240
=
0
5
x
4
−
60
x
2
+
240
=
0
x
2
−
12
x
2
+
48
=
0
D<0
So, f(n) is always increasing
Suggest Corrections
0
Similar questions
Q.
Let
φ
(
x
)
=
f
(
x
)
+
f
(
1
−
x
)
and
f
"
(
x
)
<
0
in
[
0
,
1
]
,
then
Q.
Let
f
(
x
)
=
2
x
2
−
l
n
|
x
|
,
x
≠
0
,
t
h
e
n
f
(
x
)
is
Q.
Consider the function
f
(
x
)
=
s
i
n
5
x
+
c
o
s
5
x
−
1
,
x
ϵ
(
0
,
π
2
)
. Which of the followind is / are correct?
Q.
If
y
=
f
(
x
)
is monotonic decreasing at
x
=
a
, then
Q.
f
(
x
)
=
x
+
1
/
x
,
x
≠
0
is monotonic increasing when -
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
MATHEMATICS
Watch in App
Explore more
Condition for Monotonically Decreasing Function
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