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VITEEE 2019 Solved Paper
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© examsnet.com
Question : 111
Total: 125
If
f
(
x
)
=
x
3
+
b
x
2
+
c
x
+
d
and
0
<
b
2
<
c
, then in
(
−
∞
,
∞
)
,
f(x) is a strictly increasing function
f(x) has local maxima
f(x) is a strictly decreasing function
f(x) is bounded
Validate
Solution:
f
(
x
)
=
x
3
+
b
x
2
+
c
x
+
d
,
(
0
<
b
2
<
c
)
∴
f
′
(
x
)
=
3
x
2
+
2
b
x
+
c
Discriminant
=
4
b
2
−
1
2
c
=
4
(
b
2
−
3
c
)
<
0
Given,
b
2
<
c
⇒
b
2
<
c
<
3
c
⇒
b
2
−
3
c
<
0
⇒
4
(
b
2
−
3
c
)
<
0
∴
f
′
(
x
)
>
0
∀
x
∈
R
Thus,
f
(
x
)
is strictly increasing
∀
x
∈
R
© examsnet.com
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