WEBVTT
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all right, so we're being asked to stretch to
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graph a function that satisfies all of the given conditions
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. And so we obviously have a lot of conditions
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. So I'm going to go ahead and kind of
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put this all together in a formal intervals. Easy
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the way to understand. So let's see. Let's
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start off with this stuff down here all the stuff
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. That's a lot of interval stuff. So we're
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goingto see. So says the derivative So at front
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of X is greater than zero if zero of Weston
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access Weston to. So that means that if it's
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positive the function the graph is increasing, so is
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increasing from zero two two and then we were told
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that it is less Inger between is decreasing and this
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is occurring from negative one to zero. And then
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this is also occurring between ah, all ex Celestine
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too. So this is going to be all lessons
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all ex, lest into and less than four.
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So between two and four and and all greater than
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force often for to infinity. And then we're told
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that the limit as experts is negative to me.
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Two from the left is to part of infinity and
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from the right it's negative Infinity! So we have
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a vertical ascent. Oh, at two. Ex
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tickles too. And then we're told that the Khan
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cavities. So we're told that in this car that
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from negative one to two and between two and four
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, it is also concave down for all ex greater
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than force that I mean for to infinity. So
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now that we have all of it information we can
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could've graft this picture now. And we're also told
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that the at thes access we have a tangent.
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We have ah, attendant line of C e o
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. And we're also told that FBI director, I
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missed this information at one. It is equal to
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one, so yeah. Ah, let's go ahead
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and start drafting. Um Okay. So are critical
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for him to start from the left side. We're
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going to go from the left to the right.
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We know that it is increasing between zero and two
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and we notice decreasing between for ah, for all
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ex lesson zero and yeah, so this is gonna
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look something like this and make a new one kind
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of kind of come up. You can have a
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zero. Is gonna have a a a local,
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Max, It's going to come down. We're gonna
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have a tenant line of zero and then at Toothless
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, just labelled with that too. This is going
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to go after positive infinity. And this is going
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to come down since Meghan Infinity. So we're gonna
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have it increasing, and they're gonna have a changing
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con cabbie right here in the local max and then
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come down and this is happening at force, and
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this is a graph.