WEBVTT
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Alright, so here's an interesting question. They don't
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tell you what the function is that, they tell
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you it's continuous on the interval from 1-5 inclusive.
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And then this is an interesting thing. F uh
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The only solutions to f of X equals six Are
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one and 4. Let's start graphing. This is
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okay, so we've got six, maybe that's three
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. I'm just trying to see how big one should
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be. Okay, one and four, So we've
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got at X equals one, and X equals four
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. The value is six, and then I'm just
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going to put a dotted line here at no other
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point. Are we allowed to cross this dotted line
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? That's what this only means. The only time
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we're allowed to touch that line, Is that one
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and 4? Okay. Furthermore, we have F
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two equals eight. We have this point on the
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function and it's got to be continuous All the way
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from 1 to 5 in that hole in that whole
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interval. Okay. Um So now we're asking,
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well, what's the value at 3? Well um
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it's got to be continuous. So somehow either,
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you know, it can be as crazy as you
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want, but we've got to end up here and
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then we've got to end up here and we've got
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to end up Back down to six without crossing this
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line. So there is no way that the value
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at three could be below six and be continuous.
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If it were we would across this line and we
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haven't. Um Okay, and the fancy way of
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saying this is the intermediate value theorem. Uh Well
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, is it the no, this is not really
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the intermediate value, the intermediate value theorem is related
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, but basically we've got to be continuous. We
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can't cross this line, so um three has to
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be greater than six.