1
00:00:00;00 --> 00:00:07;08
If you ignore everything
else,it's y equals point

2
00:00:07;09 --> 00:00:09;12
five a, so that's the rate
of change of point five, it

3
00:00:09;13 --> 00:00:13;07
changed by point five every
time. The graph that was in

4
00:00:13;08 --> 00:00:17;07
your homeowork went in
interval sizes of one.

5
00:00:17;08 --> 00:00:22;11
Which you already saw that,
right? What if...turn that

6
00:00:22;12 --> 00:00:26;08
one off. Here's the same
equation, only interval

7
00:00:26;09 --> 00:00:37;00
sizes of point five. That's
the same, y equals point

8
00:00:37;01 --> 00:00:39;09
five a, y equals point five
a, so everything is still

9
00:00:39;10 --> 00:00:42;11
the same. Except now the
steps, your rates of

10
00:00:42;12 --> 00:00:47;00
change, change every what
interval? Point five

11
00:00:47;01 --> 00:00:49;05
interval. Whereas in your
homework they changed every

12
00:00:49;06 --> 00:00:55;13
whole interval. How do you
think that would affect the

13
00:00:55;14 --> 00:01:00;03
graph you drew on the bottom? Instead of being

14
00:01:00;04 --> 00:01:04;05
step size one being in step size, this is the same

15
00:01:04;06 --> 00:01:07;14
thing, only point fives. How do you think that would

16
00:01:07;15 --> 00:01:09;14
affect the graph that we just talked about in the

17
00:01:09;15 --> 00:01:12;04
very last problem of your homework?

18
00:01:23;07 --> 00:01:25;14
[Wouldn't it just make
the points smaller?]

19
00:01:25;14 --> 00:01:28;05
What do you mean make
the points smaller?

20
00:01:28;06 --> 00:01:31;12
[Like, instead of it being
two to three, it would be]

21
00:01:31;13 --> 00:01:34;06
[three and a half, so
there'd just be another]

22
00;01:34;07 --> 00:01:37;10
[point there. It wouldn't
really change very much.]

23
00:01:48;06 --> 00:01:49;03
What did we say?

24
00:01:49;04 --> 00:01:51;10
It would go up to one
and a half this time.

25
00:01:58;01 --> 00:02:01;03
Okay, so there's three
points that I roughly

26
00:02:01;04 --> 00:02:05;00
resketched. So tell me what
you're talking about, Ryan.

27
00:02:05;01 --> 00:02:08;12
[If you went over it just
past one of the points...]

28
00:02:08;13 --> 00:02:12;04
So instead of going all
the way over to one,

29
00:02:12;05 --> 00:02:14;10
I'd have what going on
at a half?

30
00:02:14;11 --> 00:02:15;13
[Just another point.]

31
00:02:15;14 --> 00:02:18;03
Another point where?
Just on this line?

32
00:02:18;04 --> 00:02:20;00
[Yeah.]

33
00:02:28;09 --> 00:02:32;09
So at point five, the rate
of change is still zero.

34
00:02:32;10 --> 00:02:34;04
There's point five,

35
00:02:34;05 --> 00:02:35;08
does the rate of
change stay zero?

36
00:02:40;01 --> 00:02:42;11
No, where is the rate of change at point five?

37
00:02:42;12 --> 00:02:43;11
[Goes up.]

38
00:02:43;12 --> 00:02:46;06
It goes up according to
this. If'll be point five

39
00:02:46;07 --> 00:02:51;02
times point five. So
before, with step size one,

40
00:02:51;03 --> 00:02:53;09
it was at zero, but at
step size a half,

41
00:02:53;10 --> 00:02:55;07
this point would go where?

42
00:03:00;04 --> 00:03:03;11
Up a little bit. Would this point still be there?

43
00:03:24;07 --> 00:03:28;01
Is the rate of change at
one? In this interval size

44
00:03:28;02 --> 00:03:33;12
still zero? No, where would
it go? Up a little bit.

45
00:03:33;13 --> 00:03:37;07
What about in there?

46
00:03:42;05 --> 00:03:49;03
Up a little bit. Okay, so
will it still be choppy

47
00:03:49;04 --> 00:03:51;03
though? Like will it still
be these little segments

48
00:03:51;04 --> 00:03:58;05
getting connected? Yeah,
but how so? How would the

49
00:03:58;05 --> 00:04:03;02
segments getting connected
in this case, differ from

50
00:04:03;03 --> 00:04:05;09
the segments that we
already connected in the

51
00:04:05;10 --> 00:04:08;13
first case? They'll still
be segmented. We saw it

52
00:04:08;14 --> 00:04:12;00
won't be identical because
the rates of change are

53
00:04:12;01 --> 00:04:16;04
changing at point five
interval size. They change

54
00:04:16;05 --> 00:04:19;06
more often. It does create
more points, yes Ryan.

55
00:04:19;07 --> 00:04:24;12
Still creates a segmented
graph, but how does it

56
00:04:24;13 --> 00:04:27;00
differ from the one we
already drew? Mr. Gromic?

57
00:04:27;01 --> 00:04:29;14
[More specific, I guess.]

58
00:04:29;15 --> 00:04:33;09
Okay, tell me why you think it would be more specific.

60
00:04:33;10 --> 00:04:39;10
[Because since there's
more dots, I guess.]

61
00:04:45;09 --> 00:04:47;07
Okay, so Mr. Gromic thinks
it's gonna start to get

62
00:04:47;08 --> 00:04:50;00
more specific because we're
including more points.

63
00:04:50;01 --> 00:04:53;11
We're starting to look at
more rate of change

64
00:04:53;12 --> 00:04:58;10
intervals. Good. More
specific implies to me that

65
00:04:58;11 --> 00:05:00;02
it's approaching something.

66
00:05:00;03 --> 00:05:03;01
What would be the most specific case possible.