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35.
Possible answers:
(a)
(b)
[
2
2, 4] by [
2
2, 4]
[
2
1, 4] by [0, 3.5]
(c)
[
2
1, 4] by [0, 3.5]
36.
Possible answers:
(a)
(b)
[
2
1, 5] by [
2
2, 4]
[
2
1, 5] by [
2
1, 8]
(c)
(d)
[
2
1, 5] by [
2
1, 8]
[
2
1, 5] by [
2
1, 8]
37.
One possible answer:
[
2
3, 3] by [
2
15, 15]
38.
One possible answer:
[
2
3, 3] by [
2
70, 70]
39.
Because the trucker’s average speed was 79.5 mph, and by
the Mean Value Theorem, the trucker must have been going
that speed at least once during the trip.
40.
Let
f
(
t
) denote the temperature indicated after
t
seconds.
We assume that
f
9
(
t
) is defined and continuous for
0
#
t
#
20. The average rate of change is 10.6
8
F/sec.
Therefore, by the Mean Value Theorem,
f
9
(
c
)
5
10.6
8
F/sec
for some value of
c
in [0, 20]. Since the temperature was
constant before
t
5
0, we also know that
f
9
(0)
5
0
8
F/min.
But
f
9
is continuous, so by the Intermediate Value Theorem,
the rate of change
f
9
(t) must have been 10.1
8
F/sec at some
moment during the interval.
41.
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 Fall '08
 GERMAN
 Mean Value Theorem

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