MathDB
Problems
Contests
Undergraduate contests
Putnam
1987 Putnam
A3
Putnam 1987 A3
Putnam 1987 A3
Source:
August 5, 2019
Putnam
Problem Statement
For all real
x
x
x
, the real-valued function
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
satisfies
y
′
′
−
2
y
′
+
y
=
2
e
x
.
y''-2y'+y=2e^x.
y
′′
−
2
y
′
+
y
=
2
e
x
.
(a) If
f
(
x
)
>
0
f(x)>0
f
(
x
)
>
0
for all real
x
x
x
, must
f
′
(
x
)
>
0
f'(x) > 0
f
′
(
x
)
>
0
for all real
x
x
x
? Explain. (b) If
f
′
(
x
)
>
0
f'(x)>0
f
′
(
x
)
>
0
for all real
x
x
x
, must
f
(
x
)
>
0
f(x) > 0
f
(
x
)
>
0
for all real
x
x
x
? Explain.
Back to Problems
View on AoPS