WEBVTT
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All right, let's go through this problem we have
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. Why is equal to two plus X minus five
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Cube in the question is asking Show that X equals
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to five gives you the derivative equals to zero.
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But when I plug in five, why will end
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up being two and five comments to is not going
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to be a maximum or minimum. So one of
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those things that I mentioned that those air called a
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saddle point. Okay, so let's figure out what
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why Prime is equal to first two disappears. So
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this will be three times X minus five quantity squared
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. The derivative of insight is one, so we
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don't need to care about that now. If this
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is equal to zero, it's very easy to calculate
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that X is equal to five. So that part
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, I'm sure you can follow so well, like
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Prime is equal to zero at X equals 25 So
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why is it that this is not going to be
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a maximum or minimum? Uh, the precise definition
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off how ah local maximum and minimum appears Is that
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the slow pass to be zero off course? Why
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prime is going to be zero. But the sign
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has to change at the point, so from negative
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to positive or positive to negative. So if you
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look at the graph off three times X minus five
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, squared at X equals to five. The graph
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looks roughly like this, and as you can see
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that the sign doesn't change here. It's positive values
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here in positive values there, even though why prime
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is equal to zero. So what happens in the
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graph off the original one? Let's show you,
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you can see that it increases over here, but
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it's still increases there, even though the slope it's
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momentarily equal to zero at X equals 25 So that's
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one of the things that could happen just because the
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derivative is equal to zero. That doesn't necessarily mean
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that you will have a local maximum or a minimum
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, and that's how you showed this problem.