1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Change of Variables
Find the inte...
Question
Find the intervals in which f(x) = (x + 2) e
−x
is increasing or decreasing.
Open in App
Solution
f
x
=
x
+
2
e
-
x
f
'
x
=
-
e
-
x
x
+
2
+
e
-
x
=
-
x
e
-
x
-
2
e
-
x
+
e
-
x
=
-
x
e
-
x
-
e
-
x
=
e
-
x
-
x
-
1
For
f
(
x
) to be increasing, we must have
f
'
x
>
0
⇒
e
-
x
-
x
-
1
>
0
⇒
-
x
-
1
>
0
∵
e
-
x
>
0
,
∀
x
∈
R
⇒
-
x
>
1
⇒
x
<
-
1
⇒
x
∈
-
∞
,
-
1
So,
f
(
x
)
is increasing on
-
∞
,
-
1
.
For
f
(
x
) to be decreasing, we must have
f
'
x
<
0
⇒
e
-
x
-
x
-
1
<
0
⇒
-
x
-
1
<
0
∵
e
-
x
>
0
,
∀
x
∈
R
⇒
-
x
<
1
⇒
x
>
-
1
⇒
x
∈
-
1
,
∞
So,
f
(
x
)
is decreasing on
-
1
,
∞
.
Suggest Corrections
0
Similar questions
Q.
Find the intervals in which f(x) = log (1 + x) −
x
1
+
x
is increasing or decreasing.
Q.
Find the intervals in which the function
f
(
x
)
=
log
(
1
+
x
)
−
2
x
2
+
x
is increasing or decreasing.
Q.
Find the intervals in which the function
f
(
x
)
=
(
x
−
1
)
(
x
−
2
)
2
is increasing or decreasing.
Q.
Find the intervals in which
f
(
x
)
=
(
x
+
1
)
3
(
x
−
3
)
3
is increasing and decreasing.
Q.
Find the interval in which the function
f
(
x
)
=
(
x
+
1
)
3
−
(
x
−
3
)
3
is strictly increasing or decreasing
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
Change of Variables
MATHEMATICS
Watch in App
Explore more
Change of Variables
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