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Putnam
1962 Putnam
A4
Putnam 1962 A4
Putnam 1962 A4
Source: Putnam 1962
May 15, 2022
Putnam
Derivatives
inequalities
Problem Statement
Assume that
∣
f
(
x
)
∣
≤
1
|f(x)|\leq 1
∣
f
(
x
)
∣
≤
1
and
∣
f
′
′
(
x
)
∣
≤
1
|f''(x)|\leq 1
∣
f
′′
(
x
)
∣
≤
1
for all
x
x
x
on an interval of length at least
2.
2.
2.
Show that
∣
f
′
(
x
)
∣
≤
2
|f'(x)|\leq 2
∣
f
′
(
x
)
∣
≤
2
on the interval.
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