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Mathematics
Mathematics
Problem
For the family of functions
h
k
(
x
)
=
x
3
−
3
k
x
2
h_k(x)=x^{3}-3kx^{2}
h
k
(
x
)
=
x
3
−
3
k
x
2
, determine the set of all real values of
k
k
k
for which
h
k
h_k
h
k
is increasing on the entire interval
(
0
,
4
)
(0,4)
(
0
,
4
)
. a)
k
<
2
k<2
k
<
2
b)
k
≤
0
k\le 0
k
≤
0
c)
k
<
0
k<0
k
<
0
d)
k
>
0
k>0
k
>
0
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