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Mathematics
Problem
Let
f
(
x
)
=
x
2
+
2
k
x
+
1
f(x)=x^{2}+2kx+1
f
(
x
)
=
x
2
+
2
k
x
+
1
be defined on the closed interval
[
0
,
2
]
[0,2]
[
0
,
2
]
. Determine all real values of
k
k
k
for which
f
f
f
is strictly increasing on
[
0
,
2
]
[0,2]
[
0
,
2
]
.
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