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Some random rate of change
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[How to find a point?] No how to
find the whole function
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for number one given that information.
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Do you want that function or how to do it?
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[I'm so confused]
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Just i want the function which
is the whole thing
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y equals
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hx plus parentheses negative j
parentheses h close it plus j
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ok
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yes very good
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we kind of spat this out at the
very end of the hour.
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ladies and gents I want to make sure
you are understanding not only how
these pieces come into play
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but how these pieces come into
play graphically
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so you can write this down if you want to,
you don't have to
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I just want to make sure we are all
making the same connections
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here in terms of how we write it
algebraically.
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How we represent it graphically.
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K so I am just going to have
some random point.
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And you know if i use the same
ordered pair as
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what we did in number one it would
be some random point j comma k.
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alright
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And then eventually you know you
are going to have a line that
passes through this point.
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Soo...
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There
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K
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When you guys are defining a function
for a constant rate of change
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situation.
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Your constant rate of change comes
into play
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how, with this function definition?
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What is your constant rate of change
represented by up here?
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Come on where does the rate of
change go?
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We are doing it uppities
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Go ahead say it [h]
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H yes this is your constant
rate of change.
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Now this value whatever it is,
is what?
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Once you know what that value is
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what does it represent?
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Um not the change in y, the change in y
is in there but i mean the whole
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thing once you take this product and you
add it to whatever k is what you have
when it is done.
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What does that represent what are you
looking for when you are doing all
of this jazz.
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Ooo
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K what form are we trying to
write our equation
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in, y equals [mx] mx plus b we already
said we know what m is what's that b
value this value is the value of b, what is that?
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John? [Initial value] Initial value yes
so initial value how, what is so special
about being an initial value?
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Where y is, something like that
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[Where it starts] Ok where it starts,
what does it mean to start again?
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there it is, Katie. [One x is zero]
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So where, I am actually going
to pick on Katie, go circle on my graph
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Just go circle on my graph
where the value is
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I know we do not know what it is just
go circle what it looks like.
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What the initial value or
what the b value
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looks like on a graph
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Do you agree with Katie?
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Ok good, so she circled the point
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She circled the value when x is zero,
if I were to write this ordered
pair it would be zero comma
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Something, k so that is what it looks
like so think about this ladies and gents.
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What you're given in these situations,
for instance I gave you j comma k.
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You know
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That height, that value of the function,
you know this value of the function
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But what you need
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Is that
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value of the function
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Does that make sense?
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What you are given in your point
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Is
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whatever that is
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what you are looking for is that value
or that distance or whatever
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When x is zero, you are looking for that
value so you have this, you need that.
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K
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And the question is how do you get there?
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K and we have been doing a lot of them and
you guys have gotten pretty good
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at just crunching some numbers and
that is good
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But you have to also
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kind of know what you are crunching
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when you are crunching your numbers
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so this is visually, j comma k is this
point this is the value that you know.
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This is the value that you need
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what you know, what you need
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Yes, ok so
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can you see
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how this value and this case fall
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short of the one that we need, this value
that you know is less than than
the value that you need, yes?
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So
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in a sense what you are looking for is
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kind of that gap
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K cause you already know how high this
point is, you are already given j comma k.
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If this is three comma four
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you know this value is four.
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If this is a .2 comma 8
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you know this value is 8
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So you already this at least much of it.
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What you don't know is this
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change, how much do you have to change by
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to be that.
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K so what you need is this
change so that you can
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add it on.
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Make sense?
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Marissa kind of reiterate
what I just said, in your own words.
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Find the change [What about the change?]
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That
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I am not sure.
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well do not use the same words as me just
what is this picture trying to
get across. [You are trying]
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[to go from 0 to point JK]
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[You have to find the difference
between them]
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[I guess]
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Ok find them yea, what about that
difference though?
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Once you have the difference is
that going to be this?
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[Yea]
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Nope
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[No]
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Sabrina?
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[The rest of that is going to
make that equal, the part that
is added onto it.]
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Right when you find the difference Marissa
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You are finding that change, that amount,
that gap almost.
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But once you find that gap
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You need to add it on to what
you already have.
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K so what you were talking about
Marissa is this piece of it.
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K the gap so to speak
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between what you know and
what you need.
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But that gap alone is not your answer
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this gap versus what you need as a
whole this gap gets added on
to what you already know.
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K so good, good.
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Ok
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Here is pictorally
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what you are looking for,
you need this change so you can tack
it onto what you already know.
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Then you get your initial value.
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But the question is how to get that change
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remember we know this because you are
given a point J comma K we know this,
this is good to go this is just a number.
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But what you do not know is the change.
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K that is what you have to figure out
so that you can tack it on.
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So remember your calculus triangles
you have been drawing your little dot dot dot,
and you dot dot dot.
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This is a point that you know,
Katie circled the point we
would like to have.
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K point you know, point you
would like to have.
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So you can think about your calculus
triangles in there again.
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How much
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did I change
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in the x direction
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if I am at J comma K.
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How much do you have to change
in the x direction
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if I am at J comma K
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in order to get to that next point
that Katie drew for us.
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[J]
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Well very close, extremely close,
Danielle? [negative J] Negative J
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K you are currently at J whatever that is
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you would like to change negative J
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so you need to change
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negative J in order to get to Katie's point
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How will the
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y direction
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change if you change the x's by negative j
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how will the y value then change
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[It will be k times as much]
How many times as much? [k]
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00:09:39,643 --> 00:09:43,639
[or j, k yea k]
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Class is all correct, can you
say it again [h] ok why h?
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00:09:50,466 --> 00:09:55,664
Why h times as much, you are all right,
but why h times as much Greg?
[it is your rate of change]
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Yea that is your rate of change,
this value tells you exactly how to change.
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That is your rate of change.
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So if ever you are asking yourself
how much does this change
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00:10:06,947 --> 00:10:11,419
You are looking for in respect
to your rate of change.
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So if your x value changed by negative J.
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Your y value changes, say it again class
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[h times as much] H times as much exactly
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Well h times as much of what.
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00:10:25,397 --> 00:10:30,668
h times as much, h times as much of what?
165
00:10:44,235 --> 00:10:49,187
[what is the question?] The question
is you were all correct when you said
it changes h times as much
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but h times as much of what?
167
00:10:55,400 --> 00:10:58,826
I hear mumbling what are you all saying?
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If you are wrong let's talk about it,
I heard a couple people say something
I just couldn't catch it.
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Forbes?
170
00:11:08,948 --> 00:11:14,711
[negative j] K you are correct,
why negative j?
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00:11:34,171 --> 00:11:42,506
[I guess because the y change is h times
as much and h is the value of the x.]
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00:11:42,506 --> 00:11:45,323
Very good.
