WEBVTT
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Okay. We want to draw a graph of a
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function that has these qualities. So the only point
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that we know for sure that's on the graph is
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given by this one right here. What which says
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when x zero? Y is zero. So it
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goes through the 00.0. So there it is.
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Okay, so since this is all bunched around 01
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and two, let's let's make this be one.
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This will be to this will be three. Run
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23. Okay. The next thing we know is
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that the derivative at zero equals three. Okay.
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So what that says is this At X equals zero
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. The slope of the tangent line to f Is
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3/1. So I have to drop, I'm gonna
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draw the tangent line and it's got to touch this
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red dot and a slope has to be 3/1.
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So I'm just gonna go ahead and do that up
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. 3/1. Okay, so here's the tangent line
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. Okay, that's not part of the function.
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That's just the tangent line. Okay, so the
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red part is going to be the function. So
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here comes the function. What's it doing down here
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? I don't know. Okay, we don't have
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any information so we just ignore that. Okay,
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so it's got to go through that point and it's
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got to be tangent. See that green dotted line
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? Yeah. Okay. Now the next one says
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when it gets to one, The slope of the
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Tangent Line is zero. Okay. So how where
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is it when it gets to one is it at
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Y equals one. Is that y equals two?
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We don't know. Just make it go there Can
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it? When it gets to one The Tangent Line
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has to have slope zero. So here's the new
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tangent line. This one has chemical zero. This
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one had chemicals three. So when that red function
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gets to one it has to stop and then turn
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around and go back down. Okay? Because the
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tangent line can only touch it once and it can't
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cross through it at that point it can cross through
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it later but it can't cross through it now.
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All right now when we get to to the slope
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of the tangent line has to be negative one.
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Okay? So let's say it's gonna get to right
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here then the slope has to be negative one right
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there. So well it's oops come back. Yeah
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let's make it get right on one right here.
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Okay so when it gets there it's tangent line has
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to have slope negative one. So down line over
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one down 1/1 has slope negative one. So when
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we get to that red point we have to come
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up to that tangent line, touch it and then
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move on. Oh my kind of touching more than
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one place. I'd better fix that. I needed
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to touch right on it and then go off and
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then it could cross over later. All right so
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What's it doing after this? I don't know what's
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it doing before this? I don't know all I
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know is that it goes through 00. Is tangent
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line there has sloped three. Its tangent line at
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one is has slope zero and its tangent line at
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X equals two has slope negative one. That's a
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graph. So if you look in the back of
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the answers in the back might not look exactly like
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that. Okay, But look for the important things
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. What's happening at zero? What's happening at one
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? What's happening at two? Okay. Hope that
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helps. It's hard when you first start but you'll
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get it.