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Mathematics
Mathematics
Problem
Consider
f
(
x
)
=
x
4
+
2
k
x
2
+
1
f(x)=x^{4}+2k x^{2}+1
f
(
x
)
=
x
4
+
2
k
x
2
+
1
, where
k
∈
R
k\in\mathbb{R}
k
∈
R
. Determine, in terms of
k
k
k
, whether the point
x
=
0
x=0
x
=
0
is a local maximum, a local minimum, or neither.
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