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Here was the rate of
change function that went

2
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with it. Explain it to me. It's
different than the one we

3
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just talked about.
But yet, the same

4
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types of things are happening. So, Joshua?

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[It's getting more positive
and then once it hits zero,]

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[it starts to get
more negative]

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I think I know what you
mean, but just tell

8
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me again and I'm
going to try to decode it.

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[On the left graph...]

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K

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[It's getting more positive.
the negatives are getting]

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[closer to zero
and less negative.]

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The negatives are
getting less negative?

14
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OK, say more.

15
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[Is that right?]

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Say more

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[Then, once it hits zero,
it starts getting...]

18
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[it's going down]

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What does that mean
for it's rate of change?

20
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[It's getting more negative]

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Go ahead, it will be...

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[Negative]

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Negative.

24
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And as it goes, is it getting
more or less negative?

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[More]

26
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More negative. Hang on,
come back over here. Amy

27
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Lynn, these are negative values,
I agree.

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But what's their
rate of change?

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[Positive?]

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Positive, why?

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[Huh?]

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How come it's a positive?

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I agree with you, how
come it's positive?

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[It's going up]

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It's increasing. So, this is
increasing. The values

36
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are negative, but this
curve is increasing.

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What type of rate of change
does that say to you

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if a curve is increasing?

39
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[Positive]

40
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Positive. Is that
confirmed over here?

41
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Here's your negative values of X.

42
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Here's their corresponding
rates of change,

43
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and what are they?

44
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[Positive]

45
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Positive. They're getting
more and more positive, but

46
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at what kind of rate?

47
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Faster rate or slower rate
as they approach zero?

48
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[Slower]

49
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Slower rate. Is this rate
smaller than the rate

50
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back here? Yes, that's
confirmed as well.

51
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So Amy Lynn, will you
get zero now,

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and the curve
starts to do what?

53
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[Decrease]

54
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Decrease, which means
what for it's rate of change?

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[Negative]

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Is that confirmed?
Negative rates of changes?

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Tell me again how those
rates of change change?

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Are they getting more
negative or less negative?

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[More]

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More negative. Is
that confirmed?

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More

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More negative,
exactly. Good.

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Everything we just talked
about for that previous one,

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Increasing means
this for the curve,

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decreasing means
that for the curve,

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Rates of change, curve
trends, all that stuff ties

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in exactly to this,
only reversed.

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Here there's negative
values and yet it's

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increasing. Well, yeah, who
cares if they're negative?

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The rate of change,
that's what they mean that

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I just have to drill
into your head.

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These graphs that we're
representing are not just Y

73
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values. Yeah, this is
negative, but that's not

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going to show over here.
What's showing on your

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rate of change function are
your rates of change. So,

76
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don't just look at this and
say oh negative. Yeah, it's

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negative, but it's increasing.
The rate of change is

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increasing. It's positive. See
what I'm saying? Just make

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sure because that's really
going to be key, what's

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important in this is to know
that those step equations,

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Those step functions that
you're drawing, those are

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rates of changes
to describe

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how the curve changes.

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Not how the curve looks,
but how the curve changes.