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Mathematics
Mathematics
Problem
For a positive constant
k
k
k
, consider
h
k
(
x
)
=
x
2
−
4
k
x
h_k(x)=x^{2}-4kx
h
k
(
x
)
=
x
2
−
4
k
x
on the interval
[
0
,
4
]
[0,4]
[
0
,
4
]
. For which values of
k
k
k
does
h
k
h_k
h
k
attain its absolute maximum at
x
=
4
x=4
x
=
4
? a)
k
>
2
k>2
k
>
2
b)
1
<
k
<
2
1<k<2
1
<
k
<
2
c)
0
<
k
≤
1
0<k\le 1
0
<
k
≤
1
d)
0
<
k
<
2
0<k<2
0
<
k
<
2
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