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Putnam
2015 Putnam
B1
B1
Part of
2015 Putnam
Problems
(1)
Putnam 2015 B1
Source:
12/6/2015
Let
f
f
f
be a three times differentiable function (defined on
R
\mathbb{R}
R
and real-valued) such that
f
f
f
has at least five distinct real zeros. Prove that
f
+
6
f
′
+
12
f
′
′
+
8
f
′
′
′
f+6f'+12f''+8f'''
f
+
6
f
′
+
12
f
′′
+
8
f
′′′
has at least two distinct real zeros.
Putnam
Putnam 2015
Putnam calculus