WEBVTT
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Okay, so we're being has to state the first
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and second devoted. Um, Okay, So the
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first derivative test tones is that if a prime is
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changes from negative, I'm so I would start with
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parts. Start with positive if prime changes from positive
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, too negative as my point. See, then
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it has a local Max has local time out.
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Call Max at sea. And this makes sense because
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if you think about it on the graph is increasing
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. I'm so it's scoring up. A proven there
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suddenly training to go down. You could see that
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at this point when it changes, it hasn't had
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the local Max because it is greater than all the
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points in the neighborhood. So that's why this is
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very important. So that's not important to understand visually
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. So that's what the first point, the second
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point is that a crime, it's the other way
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. So it goes from negative two positive on an
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interval, and it occurs that point C. I
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didn't have it. Has a local men has a
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woman? Oh yeah, that's C. And this
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makes sense because when you go on negative, negative
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, negative, positive, positive. The local occurs
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because this is the lowest point in the neighbourhood of
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this in the neighborhood or surrounding point. And then
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if ah farm did not change, so there's no
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change. Then there is no local Max on.
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Then there is known local maximum. And the reason
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why this is true, because if you're increasing,
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you don't know this point is the local Max,
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because we don't know if it's going up or down
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, up or down. It's just gonna be keep
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going up. And it could be a global max
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. It could be not. Not sure it all
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depends. So when we know there's no change,
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we know for a fact that's no local make no
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local matter, little man. And then for the
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second derivative test, um, we take the second
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derivative, which is part of the name. So
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if trying back is greater than zero on an interval
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, Hi, so on and terrible I then f
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fairs. Oh, I'm sorry about that. Just
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to make that I through. Then on an interval
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, I then f is Khan cave up so con
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cave up. So that's what that will be.
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The shape of the graph and this is the second
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rate of stances very helpful and helping us understand the
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shape of the craft. Um And then if it's
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a lesson zero So the second derivative, his lessons
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you on the interval I Then it is the opposite
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Witches con cave down and clanking down Looks like this
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like an upside down you Oh, con que down
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. And then the last question last part of the
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question asked us under what circumstances it inconclusive. And
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what do you do if it fails? We'Ll It
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is inconclusive. Whenever pride of X is equal to
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zero, we don't know if it's in clown tip
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off the country round. And then so then what
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we do is we were for to the first drip
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of cast because the first derivatives tests were always tell
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us what's happening first derivative. Okay. And if
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you think about it first, you really don't even
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need this. I can do everyone test because the
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first driven and test will tell you that the function
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is decreasing on descent like just do like that,
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so decreasing because this is where to decreasing. And
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this is where decreasing and in if it's increasing.
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The first report of taps you that this is increasing
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and this is increasing. So the second day of
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the test, there's really help the dead help with
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visualize what's going on and make it a lot easier
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to draw the picture. But you technically don't even
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need it. And that's why the first derivative testes
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so important to you, you really only need the
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first ever all right.