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8
2005 Calculus #8: Functional Function
2005 Calculus #8: Functional Function
Source:
April 29, 2013
calculus
function
integration
Problem Statement
If
f
f
f
is a continuous real function such that
f
(
x
−
1
)
+
f
(
x
+
1
)
≥
x
+
f
(
x
)
f(x-1) + f(x+1) \ge x + f(x)
f
(
x
−
1
)
+
f
(
x
+
1
)
≥
x
+
f
(
x
)
for all
x
x
x
, what is the minimum possible value of
∫
1
2005
f
(
x
)
d
x
\displaystyle\int_{1}^{2005} f(x) \, \mathrm{d}x
∫
1
2005
f
(
x
)
d
x
?
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