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Mathematics
Problem
Let
f
k
(
x
)
=
x
3
−
3
k
x
f_k(x)=x^{3}-3kx
f
k
(
x
)
=
x
3
−
3
k
x
where
k
k
k
is a real parameter. Which of the following conditions on
k
k
k
is both necessary and sufficient for
f
k
f_k
f
k
to possess
one relative maximum and one relative minimum
? a)
k
≠
0
k\ne 0
k
=
0
b)
k
>
0
k>0
k
>
0
c)
k
≥
0
k\ge 0
k
≥
0
d)
k
>
1
k>1
k
>
1
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