for-each-of-the-numbers-a-b-c-d-r-and-s-state-whether-the-function-whose-graph-is-shown-has-an-abs-2

Name: for each of the numbers a b c d r and s state whether the function whose graph is shown has an abs 2
Uploaded: 2021-07-03
Duration: 3 min 42 s
Channel: Numerade
Description: For each of the numbers $ a $, $ b $, $ c $, $ d $, $ r $, and $ s $, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum.

Question

For each of the numbers $ a $, $ b $, $ c $, $ d $, $ r $, and $ s $, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum.

Gregory Higby · Accepted Answer

All right. You have to look closely at actually assumed in quite a bit because we have all these values A. B. See I&#x27;m just writing them all down the N. R. N. S. And they&#x27;re all on the X axis. And as we look closely at the graph, we have a goes up to a B. And then falls back down. Um and then goes to a higher value for C. Uh Like a middle value here goes down. Uh Let&#x27;s see that&#x27;s where D. Is is at the bottom of that curve. Although I have to be careful because the height of D. Is not as low as the height of A. Um And then the height of our is the highest. And then where does s meat? This looks like it means about where where D. Is. But I&#x27;ll just stop right there because as you look at these because a the y. Value is the lowest of all of these. Um A would be not just a relative men but it&#x27;s also an absolute man, it&#x27;s the absolute lowest point on the graph. Whereas when you look at B. Um B. As defined up here uh huh. Has a relative max but it&#x27;s not the highest point. Um And there&#x27;s no men at B. Mind. I&#x27;ll check. I guess I should clarify that there&#x27;s no max at A either. Um Well as you look at sea then um I don&#x27;t know phrase C. Is to the left of C. There&#x27;s really not a max there because it&#x27;s undefined. And so there&#x27;s none at sea. Same thing with the men, it&#x27;s smaller to the right. Whereas when you look at d on both sides, D. Is the lowest point. Uh So that would be a local man. For a relative man I would say for D. Uh And then are we could classify as both a local max and an absolute max. I use I use relative earlier and then I switched. There&#x27;s two different phrases local and absolute. Um And then relative and global. Anyway our is if you look at that it&#x27;s the highest point anywhere on the curve. So it&#x27;s a relative max or local max and an absolute max the highest on everywhere. And as far as esko s is just a little. Uh huh. Like relative to the points on either side would be a relative men. And that&#x27;s how I clarify all of those.

Oswaldo Jiménez · Answer

in this problem, we are going to state whether the following function has an absolute maximum or minimum. The local maximum or minimum or neither a maximum nor a minimum at the numbers A B c D E r s. And here is a sketch of the graph given him the textbook correspondent to these exercise. And the first thing we got to do, this type of exercise is resolved for two global extremes of the function. That is the absolute maximum and the absolute minimum. After that we go for the local extreme. So, um talking about the the absolute maximum. In that case we refer to the largest image of all the images in the domain. Function in this case is the main of the function is assumed to be what The graph suggests. That is from a two s. This interval from a two s. This is the main of the function in that domain. We gotta look at the largest of the images and in that case that happens at s because the high has find in the graph. Is this one here his point here? Now we look at the absolute minimum. Yeah. Mhm. In that response to the smallest of the images or correspondingly the lowest point in the graph and that corresponds in this case too, the much are so I see absolute me at remember we are not talking about the value here, but because we don&#x27;t have callus on the Y axis christmas to all these numbers A B C D R N S. But we are talking where decor, that&#x27;s why we&#x27;re talking about, that&#x27;s what we say at the value. So the absolute minimum, of course at are now we have already these absolute stream, the global streams of functions. Now we go for the local and let&#x27;s talk about first to local maximum. So um we can say that at sea, we have a local maximum here. Mm And that&#x27;s because uh if you look close to see that as we stay, for example, at this open interval around see and we restrain our attention on that portion of the graph. They hide his value or the largest image, that small interval around see is the image at sea. So we have a local maximum at sea. It is not the global tell me it is not the global maximum because we have already talked about the global, absolute maximum discourse, that? S because the image of s is larger than the image of C. And this is the difference between local and absolute. That is for the absolute streams, you got to look at the whole domain. So in this case, let&#x27;s see, we have a local maximum inside the into a S. We don&#x27;t have any other local maximum but we have local minimum, for example, we have local minimum uh are which in fact is the absolute minima but it&#x27;s also a local minimum in the sense that if you look close to that uh point that is near art in an interval containing art and we look at that they&#x27;re the graph only there, the smallest value is the image of art. So we have a local minimum and our we have also a local minimum. Uh B Okay. These father hero. And that is because he&#x27;s we look close to be only the smallest value of that portion of the graph is the message be. So we have these uh we can maybe use some colors too error. That is we are going to use these green for the local minimum. Better. So is green here for the local minimum, which are R and B. So that we have a local minimum. And are we have this little and the local maximum, let&#x27;s say, let&#x27;s see, let&#x27;s say it was cross like this And that&#x27;s the only one and then A. D. Which is the other point that was given. And we got to talk about A also. But at the if you look around the there is in a close interval around the it doesn&#x27;t matter how small or big is this interval? The value of the image. That is not. It&#x27;s neither the largest image nor the smallest image. That&#x27;s because we always have images that are less than the image of the and images that are larger than the image at the that&#x27;s because basically the function is decreasing an interval around the Yeah, I&#x27;m sufficiently close to the so A D. We don&#x27;t have neither. We have neither uh maximum. Lower minimum at the but at a what happens at a. So it&#x27;s important to talk about that at a we have the same situation as the we cannot say we have a local maximum at a because we don&#x27;t have craft to the left of me so we cannot look around a both sides. So we don&#x27;t have neither maximum or minimum pay. So here at the end and also had a okay we can say that the absolute maximum s is not a local maximum and that&#x27;s the same reason for why at a we don&#x27;t have neither maximum or minimum but because we have an absolute maximum our at S we still with that better. But the only point remained to classify or top Caldas de which is neither a maximum very minimum there at a where is the same situation as the. Okay so these are all the points we needed to classify. So um this is the answer to this problem. Yeah.

Clarissa Noh · Answer

it&#x27;s clear. So when you married here, so see is a number and the Domaine de of the function f than ever sees the absolute Maxima. If FC is bigger, equal to ffx for all ex Andy, it&#x27;s absolute minima. If FC is big, smaller or equal to F effects for all ex Andy, it&#x27;s a local minima. If fo seized bigger equal to f of X when X is near, see ah, local minima of FC a smaller equal to effort facts when access near sea. So you think this information from the graph with the tell the f r is gonna be an absolute maximum an f a A is gonna be an absolute minimum, f b. It&#x27;s gonna be a local maximum an f d and F f s our local minimum and F A C is neither

Jonathon Brumley · Answer

looking at this graph in determining where we have local extreme a first for the local maximums, the highest point we have iess functionality we have is here where the X value is zero. The function value for that point is three. So there is a local maximum at X equals three and the function sorry X equals zero and the function value when x zero is three. There are two different local minimums. The smallest y values are here on the X axis. There are local minimums at X equals negative two in positive too. And for both of those points, the function value is zero.

Jonathon Brumley · Answer

and looking for a local extreme, which is where we&#x27;ve got direction changes for the local max. There is one that&#x27;s right here because that&#x27;s where the the there&#x27;s a change in direction from where it goes from up to down. We have a relative or local Max at X equals zero, and the function value when X is zero, is to There are two minimums here and here again. We have direction changes there but is changing from a decreasing to an increasing function. So we have local or relative minimums at X equals negative one and positive one, and the function values at negative one positive one are both zero.

Jonathon Brumley · Answer

and examining this graph for local extreme A. We can see that there is a point where the slope is changing from being positive to negative. That&#x27;s right here so that point death represent our local maximum. The X value A. What&#x27;s that local max occurs is once there&#x27;s a local max at X equals one and the function Sorry, that&#x27;s X equals pi over two, not X equals one. Make sure we put the X value. The function value at that point is one. There&#x27;s also a local minimum. That&#x27;s where it changes from a negative slope to a positive. That&#x27;s right here. That local minimum occurs when X is negative. Pi over two and the function value of negative pi over two is negative one.

Gregory Higby · Answer

The problem is for each of the numbers. ABC PR ise state Why there is a function. Who&#x27;s graph is shown hat on absolute maximum or minimum local, maximum or minimum when laser maximum nor a minimum. So from this graph, we can see one x because A it&#x27;s a function has some absolute minimum. Why this is absolute minimum maximum minimum Absolute minimum axe is equal to our function has on absolute maximum and then to the point B to function has a local marksman. Flames B is creature on X one X is close to please and t has a local minimum, so at see us so amazing

Gregory Higby · Answer

So we&#x27;re asked to look at these numbers a, B, C, D. R and s and determine what they are. So let&#x27;s give a quick, brief wrath of this. Um, we have are a value which is here. Then we have R B value, which it is right here. So this is B. This is a then this goes right here. Then we have a C value. This is C. Then we have a devalue right here. Then from there, get up here and we have our and then we go down and we have s. So what we see is that the point is going to be a local maximum if we move to the left and right, and it yields in a decrease. So we see that B is a local maximum. Even though it&#x27;s all the way down here, it&#x27;s actually considered a local maximum, because if we move to the right, we obviously are increasing. And if we move to the left, the next point over is all the way up here. So this is actually considered B is a local maximum. Then, um, what we see is see is going to be none. Yeah, because there&#x27;s obviously values below it. And above it, then we have next is we have Next is deep D is going to be a local minimum because we see that everything from here increases. Um, then we see that our so this is a local minimum, and then our is going to be a local max. Um, and that&#x27;s because we&#x27;re up. Here we go down, go down. Every point from there is decreasing. Um, And just to know, B is actually going to be a local men because everything to the right of it is increasing everything to the left of it is increasing.

Gregory Higby · Answer

So in this problem we&#x27;re given this graph and asked for each of the numbers A, B, c, D, r and S. State whether the function with this graph is an absolute maximum or minimum or local maximum or minimum, or neither of those. So let&#x27;s start with a. So a is an end point out here. And as we can tell looking at the graph, it is not an absolute max as there are other parts of the graph above it that have higher values of Y. And it&#x27;s not a minimum as there are other points below it as well. So it is neither a max nor a minimum. Okay, be so be as some kind of a minimum point but it looks like the point at our is actually lower than the point that be. So this is a local minimum. And especially since the curve is decreasing down to be going from left to right and then increasing past B. That makes it a local minimum as well. See by similar logic is going to be a local maximum in here as it is a maximum because the graph is increasing as we approach, see from the left and then decreasing as we go past, see heading on toward toward the right, okay, then, D Well, D is is a decreasing curve until we get to D and then it continues to decrease on past it. So D is neither a maximum nor a minimum and then our well, our is the lowest point we have of the curve. So our is both a local minimum. Right? As the graph is decreasing, going into our and then increases after our and it is our absolutely minimum for this function. Okay, So then the point S, as it&#x27;s an endpoint, cannot be either a local men or local max, but it is the highest point on the curve, so s. Is an absolute maximum for this function, and so there we go.

Problem

Use the graph to state the absolute and local max…

Problem 4 Easy Difficulty

For each of the numbers $ a $, $ b $, $ c $, $ d $, $ r $, and $ s $, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum.

Answer

$a$ is absolute mini ma, but no local mini ma.$\\$
$b$ is local maxi ma$\\$
$c$ is None$\\$
$d$ is local mini ma$\\$
$r$ is local and absolute maxi ma$\\$
$s$ is None

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$a$ is absolute mini ma, but no local mini ma.$\\$$b$ is local maxi ma$\\$$c$ is None$\\$$d$ is local mini ma$\\$$r$ is local and absolute maxi ma$\\$$s$ is None

Calculus

Grace H.

Heather Z.

Kayleah T.

Michael J.

Integration Review - Intro

Definite vs Indefinite

James StewartCalculus

Grace H.

Heather Z.

Kayleah T.

Michael J.

$a$ is absolute mini ma, but no local mini ma.$\\$
$b$ is local maxi ma$\\$
$c$ is None$\\$
$d$ is local mini ma$\\$
$r$ is local and absolute maxi ma$\\$
$s$ is None

James Stewart

Calculus