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Mathematics
Problem
Q5. Let the function
f
(
x
)
=
x
3
+
3
x
+
3
f(x) = \frac{x}{3} + \frac{3}{x} + 3
f
(
x
)
=
3
x
+
x
3
+
3
,
x
≠
0
x \neq 0
x
=
0
be strictly increasing in
(
−
∞
,
α
1
)
∪
(
α
2
,
∞
)
(-\infty, \alpha_1) \cup (\alpha_2, \infty)
(
−
∞
,
α
1
)
∪
(
α
2
,
∞
)
and strictly decreasing in
(
α
3
,
α
4
)
∪
(
α
4
,
α
5
)
(\alpha_3, \alpha_4) \cup (\alpha_4, \alpha_5)
(
α
3
,
α
4
)
∪
(
α
4
,
α
5
)
. Then
∑
i
=
1
5
α
i
2
\sum_{i=1}^{5} \alpha_i^2
∑
i
=
1
5
α
i
2
is equal to :-
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