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Mathematics
Mathematics
Problem
Consider
f
k
(
x
)
=
x
3
−
3
k
x
2
f_k(x)=x^{3}-3kx^{2}
f
k
(
x
)
=
x
3
−
3
k
x
2
, where
k
k
k
is a real parameter. For which values of
k
k
k
is
f
k
f_k
f
k
increasing throughout the open interval
(
0
,
2
)
(0,2)
(
0
,
2
)
? a)
0
<
k
<
1
0<k<1
0
<
k
<
1
b)
k
≤
0
k\le 0
k
≤
0
c)
k
<
0
k<0
k
<
0
d)
k
≥
1
k\ge 1
k
≥
1
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