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Mathematics
Mathematics
Problem
For the function
f
k
(
x
)
=
x
4
+
2
k
x
3
f_k(x)=x^{4}+2k x^{3}
f
k
(
x
)
=
x
4
+
2
k
x
3
, with real parameter
k
k
k
,
f
k
′
(
0
)
=
f
k
′
′
(
0
)
=
0
f_k'(0)=f_k''(0)=0
f
k
′
(
0
)
=
f
k
′′
(
0
)
=
0
. For which value of
k
k
k
is
x
=
0
x=0
x
=
0
a local minimum? a)
k
=
2
k=2
k
=
2
b)
k
=
−
1
k=-1
k
=
−
1
c)
k
=
0
k=0
k
=
0
d) Every non-zero real
k
k
k
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