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Mathematics
Mathematics
Problem
Let
f
(
x
)
f(x)
f
(
x
)
be a polynomial of degree
6
6
6
in
x
x
x
, in which the coefficient of
x
6
x^6
x
6
is unity and it has extrema at
x
=
−
1
x=-1
x
=
−
1
and
x
=
1
x=1
x
=
1
. If
lim
x
→
0
f
(
x
)
x
3
=
1
\lim_{x \rightarrow 0} \frac{f(x)}{x^3}=1
lim
x
→
0
x
3
f
(
x
)
=
1
, then
5
f
(
2
)
5f(2)
5
f
(
2
)
is equal to
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