467
Answers
701–800
Answers and Explanations
Next, set this expression equal to –33 and solve for d:
3 3
3
33
1
1 1
0
1 2
0
4
3
4 3
2
2
2
+
−
= −
+ −
= −
=
− −
= −
+
= −
d
d
d d
d d
d
d
d
(
)(
)
,
Because the interval is of the form [0, d], the only solution is d = 4.
745.
c = 3
Begin by finding the average value of the function on the given interval by
using the average value formula with a = 1, b = 3, and f x
x
x
( ) =
+
(
)
4
1
2
2
:
f
x
x
dx
x
x
x
dx
x dx
avg = −
+
(
)
=
+






=
+
(
)
∫
∫
−
1
3 1
4
1
4
2
1
2 1
2
2
1
3
2
2
2
1
3
2
1
3
∫ ∫
=
−
( )
=
− − −
(
)
=
2
1
2 3 1
3
1 1
16
3
1
3
x x
(
)
Next, set the original function equal to the average value and solve for c:
4
1
16
3
1 4
3
3
3 4
3
3
2
2
2
2
2
2
2
c
c
c
c
c
c
c
c
+
( ) =
+ =
+ =
=
±
=
Because −
=
3 c isn’t in the specified interval, the solution is c = 3.