1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Forming Inequalities from statement
Write the max...
Question
Write the maximum value of f(x) = x
1
/x
.
Open in App
Solution
Given
:
f
x
=
x
1
x
Taking
log
on
both
sides
,
we
get
log
f
x
=
1
x
log
x
Differentiating
w
.
r
.
t
.
x
,
we
get
1
f
x
f
'
x
=
-
1
x
2
log
x
+
1
x
2
⇒
f
'
x
=
f
x
1
x
2
1
-
log
x
⇒
f
'
x
=
x
1
x
1
x
2
-
1
x
2
log
x
.
.
.
1
⇒
f
'
x
=
x
1
x
-
2
1
-
log
x
For
a
local
maxima
or
a
local
minima
,
we
must
have
f
'
x
=
0
⇒
x
1
x
-
2
1
-
log
x
=
0
⇒
log
x
=
1
⇒
x
=
e
Now
,
f
'
'
x
=
x
1
x
1
x
2
-
1
x
2
log
x
2
+
x
1
x
-
2
x
3
+
2
x
3
log
x
-
1
x
3
=
x
1
x
1
x
2
-
1
x
2
log
x
2
+
x
1
x
-
3
x
3
+
2
x
3
log
x
At
x
=
e
f
'
'
e
=
e
1
e
1
e
2
-
1
e
2
log
e
2
+
e
1
e
-
3
e
3
+
2
e
3
log
e
=
-
e
1
e
1
e
3
<
0
So
,
x
=
e
is
a
point
of
local
maximum
.
Thus
,
the
maximum
value
is
given
by
f
e
=
e
1
e
Suggest Corrections
0
Similar questions
Q.
Write the maximum value of f(x) =
x
+
1
x
,
x
>
0
.
Q.
Given:
f
(
x
)
=
x
1
x
,
(
x
>
0
)
has the maximum value at
x
=
e
, then
Q.
The maximum value of
f
(
x
)
=
x
1
x
is
Q.
The maximum value of
f
(
x
)
=
x
1
+
4
x
+
x
2
is ?
Q.
The maximum value of
x
1
/
x
is
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
Forming Inequalities from statement
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