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Mathematics
Mathematics
Problem
Consider
f
(
x
)
=
x
3
−
4
x
f(x)=x^{3}-4x
f
(
x
)
=
x
3
−
4
x
on the interval
[
1
,
3
]
[1,3]
[
1
,
3
]
. For which of the following values of
k
k
k
is the equation
f
(
x
)
=
k
f(x)=k
f
(
x
)
=
k
guaranteed to have at least one solution in
(
1
,
3
)
(1,3)
(
1
,
3
)
? a)
k
=
−
3
k=-3
k
=
−
3
b)
k
=
15
k=15
k
=
15
c)
k
=
−
2
k=-2
k
=
−
2
d)
k
=
−
5
k=-5
k
=
−
5
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