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Mathematics
Mathematics
Problem
Let
f
k
(
x
)
=
k
x
f_k(x)=k x
f
k
(
x
)
=
k
x
and
g
(
x
)
=
x
2
g(x)=x^{2}
g
(
x
)
=
x
2
on
[
0
,
2
]
[0,2]
[
0
,
2
]
, where
k
k
k
is a positive real constant. For which values of
k
k
k
is the average value of
f
k
f_k
f
k
on
[
0
,
2
]
[0,2]
[
0
,
2
]
greater than the average value of
g
g
g
on the same interval? a)
k
>
2
3
k>\dfrac{2}{3}
k
>
3
2
b)
k
>
2
k>2
k
>
2
c)
k
>
4
3
k>\dfrac{4}{3}
k
>
3
4
d)
0
<
k
<
4
3
0<k<\dfrac{4}{3}
0
<
k
<
3
4
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