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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
4
+
2
k
x
2
+
1
f(x)=x^{4}+2kx^{2}+1
f
(
x
)
=
x
4
+
2
k
x
2
+
1
, where
k
∈
R
k\in\mathbb{R}
k
∈
R
. At
x
=
0
x=0
x
=
0
, we have
f
′
(
0
)
=
0
f'(0)=0
f
′
(
0
)
=
0
. For which values of
k
k
k
is
x
=
0
x=0
x
=
0
a point of local maximum of
f
f
f
? a)
k
>
0
k>0
k
>
0
b)
k
=
0
k=0
k
=
0
c)
k
<
0
k<0
k
<
0
d)
k
≠
0
k\neq 0
k
=
0
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