Part II: The Answers
468
Answers
701–800
746.
c = 25
4
Begin by finding the average value of the function on the given interval by using the
average value formula with a = 4, b = 9, and f x
x
( ) = 1 :
f
x
dx
x dx
x
avg = −
=
= ( )
=
−
(
)
=
∫
∫
−
1
9 4
1
1
5
1
5
2
2
5
9
4
2
5
4
9
1 2
4
9
1 2
4
9
Next, set the original function equal to the average value and solve for c:
1
2
5
5 2
5
2
25
4
c
c
c
c
=
=
=
=
Because c = 25
4
is in the given interval, you’ve found the solution.
747.
c = ± 2 3
3
Begin by finding the average value of the function on the given interval by using the
average value formula with a = –2, b = 2, and f
 
(x) = 5 – 3x
2
:
f
x dx
x x
avg = − −
−
(
)
=
−
(
)
=
−
−
− −
−
−
∫
1
2
2
5 3
1
4
5
1
4
5 2
2
5 2
2
2
2
3
2
2
3
( )
( ) ( )
( ) (− −
(
) )
(
=
2
1
3
)