1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Definition of Functions
Find the inte...
Question
Find the intervals of monotocity of the function
f
(
x
)
=
2
x
2
−
log
|
x
|
,
x
≠
0
.
Open in App
Solution
We have
f
(
x
)
=
2
x
2
−
log
|
x
|
,
x
≠
0
Now,
f
′
(
x
)
=
4
x
−
1
x
=
4
x
2
−
1
x
For
f
(
x
)
being monotone increasing we must have
f
′
(
x
)
≥
0
or,
4
x
2
−
1
≥
0
or,
x
∈
(
−
∞
,
−
1
2
]
∪
[
1
2
,
∞
)
For
f
(
x
)
being monotone decreasing we must have
f
′
(
x
)
≤
0
or,
4
x
2
−
1
≤
0
or,
x
∈
[
−
1
2
,
1
2
]
−
{
0
}
Suggest Corrections
0
Similar questions
Q.
On which of the following intervals is the function
f
(
x
)
=
2
x
2
−
log
|
x
|
,
x
≠
0
increasing in
Q.
Find the intervals of monotonicity of the function
y
=
2
x
2
−
log
|
x
|
,
(
x
≠
0
)
Q.
Let f be a function defined by
f
(
x
)
=
2
x
2
−
log
|
x
|
,
x
≠
0
, then
Q.
Let
f
(
x
)
=
2
x
2
−
log
|
x
|
,
x
≠
0.
Then
f
(
x
)
is
Q.
Find the intervals of monotonicity of the function
x
log
x
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
Definition of Function
MATHEMATICS
Watch in App
Explore more
Definition of 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