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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
k
x
2
+
3
x
f(x)=kx^{2}+3x
f
(
x
)
=
k
x
2
+
3
x
for
0
≤
x
≤
4
0\le x\le 4
0
≤
x
≤
4
, where
k
k
k
is a real constant. The average value of
f
f
f
on the closed interval
[
0
,
4
]
[0,4]
[
0
,
4
]
is required to be
10
10
10
. Determine the value of
k
k
k
that satisfies this condition. Show all steps in your reasoning.
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