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Question
Mathematics
Let f: R arrow R be defined as f(x)= begincases-(4/3) x3+2 x2+3 x, x>0 3 x ex , x ≤ 0 endcases. Then f is increasing function in the interval
Q. Let
f
:
R
→
R
be defined
as
f
(
x
)
=
{
−
3
4
x
3
+
2
x
2
+
3
x
,
3
x
e
x
x
>
0
,
x
≤
0
. Then
f
is increasing function in the interval
471
156
JEE Main
JEE Main 2021
Application of Derivatives
Report Error
A
(
−
2
1
,
2
)
B
(
0
,
2
)
C
(
−
1
,
2
3
)
D
(
−
3
,
−
1
)
Solution:
f
′
(
x
)
=
{
−
4
x
3
+
4
x
+
3
3
e
x
(
1
+
x
)
x
>
0
x
≤
0
For
x
>
0
,
f
′
(
x
)
=
−
4
x
2
+
4
x
+
3
f
(
x
)
is increasing in
(
−
2
1
,
2
3
)
For
x
≤
0
,
f
′
(
x
)
=
3
e
x
(
1
+
x
)
f
′
(
x
)
>
0∀
x
∈
(
−
1
,
0
)
⇒
f
(
x
)
is increasing in
(
−
1
,
0
)
So, in complete domain,
f
(
x
)
is increasing in
(
−
1
,
2
3
)