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Byju's Answer
Standard XII
Mathematics
Monotonically Increasing Functions
Find the inte...
Question
Find the intervals of increase and decrease of the following function:
f
(
x
)
=
3
x
4
+
8
x
3
+
6
x
2
+
1
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Solution
f
(
x
)
=
3
x
4
+
8
x
3
+
6
x
2
+
1
d
d
x
f
(
x
)
=
12
x
3
+
24
x
3
+
24
x
2
+
12
x
=
f
′
(
x
)
for increasing
f
′
(
x
)
>
0
⇒
12
x
(
x
2
+
2
x
+
1
)
>
0
⇒
12
x
(
x
+
1
)
2
>
0
⇒
here
x
ϵ
(
0
,
∞
)
For decreasing
f
′
(
x
)
<
0
12
x
(
x
+
1
)
2
<
0
So here internal of
x
ϵ
(
−
∞
,
0
)
.
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