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Mathematics
Problem
For the quartic
h
k
(
x
)
=
x
4
−
4
k
x
2
+
k
2
h_k(x)=x^{4}-4kx^{2}+k^{2}
h
k
(
x
)
=
x
4
−
4
k
x
2
+
k
2
, let
k
k
k
be real. Which of the following describes
all
values of
k
k
k
for which
h
k
h_k
h
k
possesses
exactly one
relative extremum? a)
k
=
0
k=0
k
=
0
b)
k
<
0
k<0
k
<
0
c)
k
≤
0
k\le 0
k
≤
0
d)
k
>
0
k>0
k
>
0
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