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Mathematics
Problem
Given
f
(
x
)
=
2
x
4
−
6
x
3
+
3
x
2
−
x
+
7
f(x)=2x^{4}-6x^{3}+3x^{2}-x+7
f
(
x
)
=
2
x
4
−
6
x
3
+
3
x
2
−
x
+
7
, derive an explicit expression for
f
(
n
)
(
x
)
f^{(n)}(x)
f
(
n
)
(
x
)
valid for every integer
n
≥
0
n\ge 0
n
≥
0
. Express your answer in closed form using factorial notation and indicate any values of
n
n
n
for which the expression is zero.
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