WEBVTT
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here we are going to sketch the graph of the
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function F of x equal one over X. For
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X greater than or equal to one. And is
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that raft to find the absolute and local maximum and
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minimum values of the function. So here we have
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made a sketch of the graph. We know that
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if that one is one At two is 1 half
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, At three is 1/3 and so on. So
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the value of the function is decreasing or not.
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My anatomically and it never stopped decreasing. That is
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always increasing. It means the graph is always approaching
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the X axis or is getting closer to it as
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we go to the right but you never cross it
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. Or that is it never gets a value that
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is on the X axis. But it's always approaching
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or getting closer to. That means that limit when
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X grows without any bound. That is what eggs
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goes to plus infinity is zero. But coming from
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positive values, that is the function is always positive
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. That's the behavior of dysfunction. And we can
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see clearly that the highest point in the graph in
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this case, that is included in the graph is
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F of one which is equal to one. So
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if of one equal one is the absolute maximum value
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of the function. That is because we have considered
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function only for X rather than or equal to one
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for A Square. That articles one. And that
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is the sort of maximum values one and is obtained
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in fact at X Equal one. So we have
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this result, we have no local maximum for this
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function remember we can consider this same value as local
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maximum because we have we don't have any graph to
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the left of the functions. So we only consider
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local streams inside of the main the endpoints of the
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interval. So in this case there is no local
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maximum, right? And there is no absolute minimum
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either has no absolute minimum or local minimum and that's
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because there is no lowest point in the graph,
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that is the graph is all with descending. It's
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never never stopped descending, so there is no longer
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with wine. The thing is that it is descendant
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but in a way that it will never touch the
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exact size of the descending, never stopped. And
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for that reason there is not the lowest point in
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the graph. And so there is no absolute medium
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and for similar situation there is no local minimum,
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so we don't have either of those. And in
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summary the function has only an absolute maximum value of
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one Attain or the course at execute one. And
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that the characteristics off or the properties of the function
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F Mexico one over X for X prison records one