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Mathematics
Mathematics
Problem
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
, where
f
f
f
satisfies the relation
f
(
x
+
y
)
=
2
f
(
x
)
+
x
f
(
y
)
+
y
f
(
x
)
∀
x
,
y
∈
R
f(x+y)=2f(x)+x f(y)+y\sqrt{f(x)}\ \forall x,y\in\mathbb{R}
f
(
x
+
y
)
=
2
f
(
x
)
+
x
f
(
y
)
+
y
f
(
x
)
∀
x
,
y
∈
R
and
f
′
(
0
)
=
0
f'(0)=0
f
′
(
0
)
=
0
. Then
f
(
6
)
f(6)
f
(
6
)
is equal to
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