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Putnam
1998 Putnam
3
1998 Putnam A3
1998 Putnam A3
Source:
April 19, 2013
Putnam
function
integration
college contests
Putnam calculus
Problem Statement
Let
f
f
f
be a real function on the real line with continuous third derivative. Prove that there exists a point
a
a
a
such that
f
(
a
)
⋅
f
′
(
a
)
⋅
f
′
′
(
a
)
⋅
f
′
′
′
(
a
)
≥
0.
f(a)\cdot f^\prime(a)\cdot f^{\prime\prime}(a)\cdot f^{\prime\prime\prime}(a)\geq 0.
f
(
a
)
⋅
f
′
(
a
)
⋅
f
′′
(
a
)
⋅
f
′′′
(
a
)
≥
0.
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