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Mathematics
Mathematics
Problem
Define
p
k
(
x
)
=
e
k
x
(
x
2
−
4
x
)
p_k(x)=e^{kx}\,(x^{2}-4x)
p
k
(
x
)
=
e
k
x
(
x
2
−
4
x
)
on the interval
(
0
,
∞
)
(0,\infty)
(
0
,
∞
)
, where
k
k
k
is a real parameter. For which values of
k
k
k
does
p
k
p_k
p
k
have
exactly two
relative extrema on
(
0
,
∞
)
(0,\infty)
(
0
,
∞
)
? a)
k
≤
0
k\le 0
k
≤
0
b)
k
<
0
k<0
k
<
0
c) All real
k
k
k
d)
k
>
0
k>0
k
>
0
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