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Putnam
1955 Putnam
B2
B2
Part of
1955 Putnam
Problems
(1)
Putnam 1955 B2
Source:
5/24/2022
Suppose that
f
f
f
is a function with two continuous derivatives 2and
f
(
0
)
=
0.
f(0) = 0.
f
(
0
)
=
0.
Prove that the function
g
,
g,
g
,
defined by
g
(
0
)
=
f
′
(
0
)
,
g
(
x
)
=
f
(
x
)
/
x
g(0) = f '(0), g(x) = f(x) / x
g
(
0
)
=
f
′
(
0
)
,
g
(
x
)
=
f
(
x
)
/
x
for
x
≠
0
,
x \ne 0,
x
=
0
,
has a continuous derivative.
Putnam