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Mathematics
Mathematics
Problem
For the family of functions
p
k
(
x
)
=
x
3
−
3
k
x
2
+
9
k
2
x
p_k(x)=x^{3}-3kx^{2}+9k^{2}x
p
k
(
x
)
=
x
3
−
3
k
x
2
+
9
k
2
x
, determine all real values of
k
k
k
such that
p
k
p_k
p
k
has exactly two relative extrema whose
x
x
x
–coordinates differ by
6
6
6
.
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