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1
2006 Calculus #1: Functional Equation in Derivatives
2006 Calculus #1: Functional Equation in Derivatives
Source:
July 30, 2012
calculus
derivative
algebra
polynomial
Problem Statement
A nonzero polynomial
f
(
x
)
f(x)
f
(
x
)
with real coefficients has the property that
f
(
x
)
=
f
′
(
x
)
f
′
′
(
x
)
f(x)=f^\prime(x)f^{\prime\prime}(x)
f
(
x
)
=
f
′
(
x
)
f
′′
(
x
)
. What is the leading coefficient of
f
(
x
)
f(x)
f
(
x
)
?
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