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Mathematics
Mathematics
Problem
Let
f
f
f
be continuous on
[
a
,
b
]
[a,b]
[
a
,
b
]
with average value
f
ˉ
\bar f
f
ˉ
. What is the average value of the function
g
(
x
)
=
f
(
x
)
+
k
g(x)=f(x)+k
g
(
x
)
=
f
(
x
)
+
k
on the same interval
[
a
,
b
]
[a,b]
[
a
,
b
]
? a)
f
ˉ
+
k
\bar f+k
f
ˉ
+
k
b)
f
ˉ
\bar f
f
ˉ
c)
f
ˉ
+
k
(
b
−
a
)
\bar f+k\,(b-a)
f
ˉ
+
k
(
b
−
a
)
d)
k
k
k
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