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Problem
Problem
Consider the cubic
f
(
x
)
=
8
x
3
+
4
a
x
2
+
2
b
x
+
a
f(x) = 8x^3 + 4ax^2 + 2bx + a
f
(
x
)
=
8
x
3
+
4
a
x
2
+
2
b
x
+
a
where
a
,
b
∈
R
a, b \in \mathbb{R}
a
,
b
∈
R
. For
a
=
1
a = 1
a
=
1
, if
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
is strictly increasing,
∀
x
∈
R
\forall x \in \mathbb{R}
∀
x
∈
R
, then maximum range of the values of
b
b
b
is a.
(
−
∞
,
1
3
]
( -\infty, \frac{1}{3} ]
(
−
∞
,
3
1
]
b.
(
1
3
,
∞
)
( \frac{1}{3}, \infty )
(
3
1
,
∞
)
c.
[
1
3
,
∞
)
[ \frac{1}{3}, \infty )
[
3
1
,
∞
)
d.
(
−
∞
,
∞
)
(-\infty, \infty)
(
−
∞
,
∞
)
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