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Sketch the graph of $ f $ by hand and use your sketch to find the absolute and local maximum and minimum values of $ f $. (Use the graphs and transformations of Section 1.2 and 1.3).

$ f(x) = 1/x $, $ 1 < x < 3 $

No absolute or local extrema

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here, we're gonna sketch the graph of the function one over X for X between one and three, not including one north three. And we will do it by hand and use that graph to find the absolute and local maximum and minimum values of the function. So we have sketched here, the function one of our X. This function is decreasing all the positive X. In fact between one and three secretion also and we don't include one or three that it it means that we have this Open circles indicating that those values that is 1/3 at three and one at one are not included in the graph. That's the graphical way to indicate that. But remember the only values that are out of the graph are just the point where X equals three and execute one. So there is no other point out of the ground. So that's the idea. And uh for the reason that their functions was decreasing and we have not included the And Points one and 3. This function has no extreme nor local. Non maximum stream at all because there's no lowest such such thing as the lowest point of the graph nor uh highest point a graph because the highest point, the graph should be at this point, but it's not included and the lowest when the graphs of VTS and is not included, we don't have also local extreme value. So we can say that f yes, no local or absolute extreme, but there is no absolute maximum, no absolute minimum, no local maximum indeed to me. And so mhm, That's the behaviour of this function in the opening about 13.

Universidad Central de Venezuela