use-the-graph-to-state-the-absolute-and-local-maximum-and-minimum-values-of-the-function-2

Name: use the graph to state the absolute and local maximum and minimum values of the function 2
Uploaded: 2018-03-15
Duration: 1 min 27 s
Channel: Numerade
Description: Use the graph to state the absolute and local maximum and minimum values of the function.

Question

Use the graph to state the absolute and local maximum and minimum values of the function.

Wen Zheng · Accepted Answer

problem is use of grass to state. It&#x27;s an absolute and the locum maximum on the minimum whiles have a function. This&#x27;s the graph from the graph. You can see the absolute maximum value is the photo, and it&#x27;s a absolute minimum. Body gets equal to one the local maximum while you years is pointed says this is for on DH three. This is that thanks to you three. It&#x27;s actually got to six on the local minimum while it is three and want to. This is I actually want you to Zac&#x27;s. You go to war.

Oswaldo Jiménez · Answer

we want to find the absolute and local maximum and minimum values of the given function. In this case of function it&#x27;s given through the graph like this. This is a sketch of the graph given in the text book but we have preserve the essential properties of the function. So we had those uh huh opens red circles and pull those like I&#x27;m talking about this one here, it is an open red red circle. This an open red circle. It&#x27;s an open research that means that the points corresponding there are not included in the graph but when we have a feel red circle like this then we know Like this one I&#x27;m talking about that the point correspondent point is inside correspond to the graft as a way of saying that graphically we have those going there and without we want to find the log the absolute extreme math extreme of the function and the local maximum minimum. So let&#x27;s start it&#x27;s always with the absolute streams which are essentially yeah, is to find. So let&#x27;s talk about the absolute maximum value and when we talk about that we are saying at the same time at which point that absolute maximum of course. And in this case we get to look at the entire domain In this case we said that the maintenance the interval from zero closed in syria because syria has emerged to because they start here, this circle is filled with red. So meaning that the point is part of the graph. So the image your is too that&#x27;s called this function F. Haven&#x27;t said it&#x27;s called F. So um The domain goes from zero All the way through seven, but 7 is open. So we came right here to the main of F is the interval from zero close at zero but open at seven. Uh And that&#x27;s why because the red circle is not filled with red. That is open, meaning that the point is not included in the graph. That&#x27;s very important. That makes a huge difference. Okay, back in all the points between Syria and seven, including Syria only uh have an image for example, the image of 123. The thing is that it is extracted or separated from the line that has a train trend here. This red line has the trend coming from the left and then continued from the right but that specifically point specifically point. Uh one the image has been instructed we were expecting for but it was um got out of the trend of the line and put at high three. That is the image of 13 Now in this graph. And what happened at six, he said the from the left graph stopped here including the point and continues then at this point, but not including the point because number six get to have only one image can have two images because in that case we won&#x27;t have a function. So this is a situation here a little bit. And then with that in mind We look at the whole domain that is from 0-7, including Syria and not seven. Um to uh find the absolute maximum value and in this case would be the highest value or the largest value of f possible. In this case we can see that that happens at four. And the values five correspondent to in the draft at this point here. So the absolute maximum value is yeah, if at four which is equal to five. So the accident actually, maximum, body is five and it&#x27;s attained or course at x equals four. Now, let&#x27;s talk about the absolute minimum in this case, respected these to be this, as the graphic suggest, is the lowest value of the lowest point in the grass. That is the smallest value of the function. But the problem here is that the point here is not included, seven is not in the domain. So, uh we can say that the function decreases all the time getting near seven but never reaches an image at that point. And for that reason, there is no absolute minimum value for this function. So this absolute minimum does not exist. And that&#x27;s very important to understand the only way that this absolute minimum B one at 7 is that we include the point to the graph, that is if we do something like this, including the point, but because we don&#x27;t have that, that is t point is excluded explicitly by not feeling the circle, we can say that there is no lowest possible value to the graph or equivalently absolute minimum value for this function does not exist. Let&#x27;s talk about local for example local maximum. So local maximum at the dysfunction is for example at four. It is at four this point here. Is that the global or absolute maximum we saw here, but it&#x27;s also local Maximum because if we look close or near the value four here, that is, we look only a portion of the graph. Years, the function we see that in effect again, the highest value of the largest values of function is five attained at four. So before we have a local maximum But there is another one Let&#x27;s say at at six we have again uh local maximum If at six and the image of six is 4 because that value is included in the graph. Because we have the field circle here. Just So the image of six is four and that&#x27;s a local uh let&#x27;s see this fight. Sorry to remarked upon in green And if you look close to six Oh near six, we consider that the largest image Or value of the function is effectively four at 6. So it was the local maximum. Okay, and there are no more local maximum because one happens. Another thing that we&#x27;re going to talk right now. So first let&#x27;s go to the local minimum now local minimum and we can see that the local minimum, let&#x27;s put it in blue, we have one here because if we look around five close to five, we can see that this modest value of the function is the image at five precisely. Which is three. So there&#x27;s a local minimum if At five equal 3. But there is another one. Um here, let&#x27;s say these founders put it in blue around this point. There is local minimum. If you look close to value to we have local minimum. That case we got to talk about. Mm hmm. But we need your mouth. Okay, let&#x27;s put it uh huh. Back here and above was also there are two values and we can talk about, oh that&#x27;s me At four FF 40 564. And local minimum is 5.3. Yeah, I&#x27;m the one and 2 if I had to equal equal to and add one, The image of 1, 3. Because the point is uh huh Good. A party trend line that is this point here is not including the graph of the point is who has been put here down here. And then You&#x27;re saying is that we look close to one and in this case Remembrance, it is important to look close to the point that we don&#x27;t need to go far from the point. We always got to be and we think near the point. So we look close to the number one. We can see that the graph is something like this and the point a separate point at one Who&#x27;s in that? She&#x27;s three. So we can say they&#x27;re looking closely to want the value Effort Wanna Go three is a local minimum. So we got to put it in the local minimum list. So we have ever six f sorry, efforts, five equal three local minimum, same thing for effort to local minimum. And F at one equals 3. So we have three local minimum and two local maximum. And of course we have an absolute maximum value Effort for Article five and there is no actual minimum value of the function Because seven is not included in the domain.

Katelyn Chen · Answer

for this question, we given ffx people tonight of one over X and we&#x27;re Asif on absolute extreme rallyists or absolute maximums and minimums on the interval from than you to disaster able to act such as lost in equal to negative one. Now another dysfunctions continuous A. There&#x27;s no minimums or maximums on this interval so we can go ahead. Just plug in our numbers. So we have a evening two is equal to this will be wilder and I get one learning to which is equal to 1/2. Then we have us with 91 which is equal to maybe have one over negative one which is equal to one. So we have our absolute then mom. But what half under absolute maximum, not one. The next time we need to do is in photographed this So we have made it one over X. I&#x27;m a *** too, which is of Leicester equal extra success in equal to named of one. And so actually weaken your half has people to 0.5. So consider this over here is 0.5 so we can find out our absolute minimum is that 0.5 and absolute maximum is that one

Katelyn Chen · Answer

this question were given the function after vax Eagle two X squared minus one onto interval from night of one is not able to x, which is lost people to to when were asked to find the absolute extreme bodies which is our absolute maximum in are absolutely love. So start off with when I find any critical number is so we know that this is a derivative of your backs off prime of X is equal to using. All right, let&#x27;s see, We can take our two new friends and we drop our drop Our power to get us to X and two X is equal to zero an exit ticket 07 state critical numbers are X equals zero. So when we&#x27;re finding our absolute maximum minimums organised our side links and then our people about loose. So we have s of negative one which is equal to maybe one squared minus one which is just equal to zero. It&#x27;s up from zero which is equal to zero squared. My swan, which is equal to native one we have to, which is equal to two squared minus 12 is equal to three and so we can see that are absolute minimum is, uh, to negative one, their absolute acts. Mom, is that three? Now? The next thing we should do is we need to cross this so we can go to does my Swede X squared minus one on the interval from We have nice one. His last three equal to X, which is Lester unequal to to And so we can see that we have our absolute minimum at zero negative one and in an absolute maximum that 23 So we so this will be our answer.

Katelyn Chen · Answer

for this question were given the function after vaccines able to for my sex cube drivel. Full night of two was Austin Able Switches Lesson. People toe one were asked upon absolute extreme values, which are absolute maximum, absolute minimum. So sterile flights we can find a critical numbers. We find a derivative of F of X, which is equal to neither three X squared. And so we need to find critical Number said is when you&#x27;re three x great, it&#x27;s equal to zero. It gets expertise. You go to zero X equal to zero. So we note our critical number is acceptable to zero so we can find out c f of our silence. Anarchic remembers. We&#x27;ve got your 20 to 4 minus 92 cubed, which is equal to four plus eight to see. Go to 12. We have one physical, two for minus one cube, which is equal to three. That&#x27;s what we have often zero she was before my hero Que, which is just equal to four. It was so consider absolute mineral. His three. Your absolute lacks wound. I was 12. Next we&#x27;re asked a graph this so we have. Let&#x27;s see quarrel mice X cubed from May Give to is less than or equal Teoh X, which is a strangle 21 So we&#x27;ve got aircraft. You can see there are minimum because right there at 13 your maximum absent maximum because the negative to 12 it&#x27;s like it&#x27;s absolutely at wise Eclipse Syria Absolute Lex, move where is equal to 12?

Katelyn Chen · Answer

for this question were given effort. Faxes equals and I did one over X scored on just 10.5 was lost Earnings X, which is lost or equal to two and were asked to find absolute extreme values. And so these air absolute maximums in the absolute minimum. So several flights. We can rewrite this as negative. Extend negative, too, which makes it easier for a Caesar parable. So then we have primer backs is equal to it. Let&#x27;s see if we can multiply this by negative to to get this to be colisee two x two Negative one dish is equal to two X, and so in a two over, accessible to zero and then one x equal to what was most by both sides but X just get to 00 So there&#x27;s just no critical numbers. And so gun based on this information me know. OK, so we have to overtax. So we&#x27;re going to say there&#x27;s no critical numbers, so we can just have while we have fo 0.5, we should big f. So he says he&#x27;s there, silent soon at those absent maximums minimums. So obey absorb what 50 to negative 1/0 500.4 squared, which is equal to mate a four into the next we have off of to What does Eagleton into 1/2 Squared is equal to number 1/4. So when you say they&#x27;re absolute, you know, occurs out there before being a absolute maximum must rewrite this as negative 0.250 after a maximum prison ended 0.25 So you next We need to grasp this. So we have I wonder, if I were X squared on the interval. No one wants that we have 2.5. Choose this English Extra sister equals two and so we can see the absolute minimum occurs. It&#x27;s negative. Four. House A maximum occurs at negative 0.25

Wen Zheng · Answer

So what? We see if we look at the graph, um, it won&#x27;t be perfect, but it&#x27;s okay. What we have here is value. It comes down to value about here. Then this comes up and goes down, and then this comes up again and goes right here. So what we see is that the absolute minimum value is clearly going to occur when X equals four. And that&#x27;s this. How you&#x27;re right here. So it&#x27;s the absolute minimum, um, and that that would also be considered a local minimum. Then we have a local maximum occurring at three. That&#x27;s right here. We also have a local maximum occurring at six. So that&#x27;s this point right here. Then. Lastly, we have our local minima, which already said, there&#x27;s one right here at X equals four, but then we also have one. Um, since there&#x27;s a point right here, this is considered a local minima at X equals two because we see that every point to the right is increasing. Every point to the left is increasing immediately thereafter.

Problem

Sketch the graph of a function $ f $ that is cont…

Problem 6 Easy Difficulty

Use the graph to state the absolute and local maximum and minimum values of the function.

Answer

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