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Mathematics
Mathematics
Problem
Let
g
(
x
)
=
x
3
+
2
x
g(x)=x^{3}+2x
g
(
x
)
=
x
3
+
2
x
. Determine all real numbers
k
k
k
for which the equation
g
(
x
)
=
k
g(x)=k
g
(
x
)
=
k
has a solution somewhere in the closed interval
[
1
,
2
]
[1,2]
[
1
,
2
]
. Express your answer as an inequality involving
k
k
k
.
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