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Mathematics
Problem
Let
g
(
x
)
=
x
2
−
6
x
+
8
g(x)=x^{2}-6x+8
g
(
x
)
=
x
2
−
6
x
+
8
be defined on the interval
[
0
,
k
]
[0,k]
[
0
,
k
]
, where
k
>
0
k>0
k
>
0
. Determine all real values of
k
k
k
for which the absolute minimum of
g
g
g
on this interval occurs at the right endpoint
x
=
k
x=k
x
=
k
.
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