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10
2005 Calculus #10: Smooth Function at 1
2005 Calculus #10: Smooth Function at 1
Source:
April 29, 2013
calculus
function
Problem Statement
Let
f
:
R
→
R
f : \mathbf{R} \to \mathbf{R}
f
:
R
→
R
be a smooth function such that
f
′
(
x
)
=
f
(
1
−
x
)
f'(x)=f(1-x)
f
′
(
x
)
=
f
(
1
−
x
)
for all
x
x
x
and
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
. Find
f
(
1
)
f(1)
f
(
1
)
.
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