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Mathematics
Problem
For
k
∈
R
k\in\mathbb{R}
k
∈
R
define
q
k
(
x
)
=
x
2
+
k
x
q_k(x)=x^{2}+kx
q
k
(
x
)
=
x
2
+
k
x
on the interval
[
0
,
3
]
[0,3]
[
0
,
3
]
. Determine all real values of
k
k
k
for which the average value of
q
k
q_k
q
k
on
[
0
,
3
]
[0,3]
[
0
,
3
]
exceeds the average value of
p
(
x
)
=
x
2
p(x)=x^{2}
p
(
x
)
=
x
2
on the same interval.
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