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3.1.49 Questlon Help Find Ina rclalivu uxtreme points 0l Iru lunchon they uXOSL Than skolcu gaph ol Ihe furicbion gix) = 343 t Idenily Jil Ihe /olulve maximum poinks SolectIro ccirod cmoreco Juand cnalco nocoY Wie #memor Dor(os) complole Dur The relalive maxiituin point{s) (Jurg (Smpilly vour answar Usc Inteqets IrucLin ns Ictuny Iuinleinine cona Ndanewus ncudod Ther rulniva mntunuma point: Wodunn ofdetod pas Uso = CDnMAo LCP Cilck Io uclecl ad Lac ycxir Jnevrer(s) wnd Ihen allck Clock pana remoinim



Answers

For Exerises $26-31$ , complete each of the following.
a. Graph each funnction by making a table of values.
b. Determine the consecutive integer values of $x$ between which each real zero is located.
C. Estimate the $x$ -coordinates at which the relative maxima and relative minima occur.
$$
f(x)=x^{5}+4 x^{4}-x^{3}-9 x^{2}+3
$$

For part A. I want you to see the graph we're going to create in the best, most graphing calculator online. This will type the function as you see it to type of expo niche. Use the keypad. And I like that you want to do 1/4 power like we need to do here, going to use the A to the P. Once you get the function in, you hide the keypad you consumed in out. If your job is to put this on graph paper, what I would recommend is I understand that behavior. But then you look the wheel and choose the table, and you want a plot values of this function, um, that are nicely core affable for you. I think that's enough. Plot the 0.6 to 5 people in 3031 500 play and plot them according to the graph here. And I think that told you plenty for you. And so that's the graph using the table now for Part B. We want to talk about zeros of the function. Zeros of the function occur when the function crosses the X axis because that's when the function is equal to zero. That's the Y value. We see that there are four of them. No, um, desk. Most will tell us what these are about, but if you were just using your graph on paper, you wouldn't be able to tell exactly. So you just need to say the integers that they're in between. So, like this 1st 1 falls between negative three negative to. You can also see this from your table because the output switch from the negative to a positive and it's continuous over. There is a zero between these two values, so we'll say between negative three and negative, too. Go to the next one. The next one occurs between negative one and zero. You can see that here because the outputs both from positive to negative there's a zero in between negative one and zero. The 3rd 1 hers here is between zero and one in the 4th 1 kers between 34 we can see again from positives and negatives between three and four, so those would be are zeros are estimations, especially during this on paper. In part C need identify rolls of maximum and minimum, so maximum are like the peaks year, so we see two of them and we can ask to me when this happens again. You are, in theory, doing this from your papers. It's not easy to see that you could say about negative 1.61 point seven and about 2.4 are the X values Where the max and what happened. I got a 1.72 point four for them are relative minimum. Here's our Menelik Valley on that is at zero. So at an X value of zero, our function hits a minimum.

Her party. I want you to see the graph that we're going to put into the dust most online graphing calculator. So once you're anti smells, we're gonna type in the function as you see it, open the keypad in the aid to be button. It will allow you to get into the export. That's how you get to the fourth power right arrow to get out of it. There's also a squared button if you don't want to type to, and once your function is there, you can hide the key pad. If you like, you can click and drag function. Know if you're transferring this to graph paper. You see how it behaves with smooth, continuous curve, but you want very specific points to plot to help guide you so quick the wheel and click the table. And you've essentially got an infinite list of values, um, to pot. So I think we've got hot enough here so you can plot the point. Negative one negative four is your negative five negative six to your negative seven very easily, and then do your past two guy the curve through those There is your graph R B. We're talking about zeros. We can see that that there are two zeros here because you're looking at the X axis zeros of the function. When the functions equals zero, which is a lie. Coordinate. This happens in two locations again. Visually, where's across the X axis? Now, if you were just referring to what paper? You can't tell exactly that this is that negative 1.21 A. You're just estimating. And so we're asked to just give the imagers of being between sensibly between negative to negative one. You could tell us from your table of values as well, because it goes from positive to negative between these two and inputs. And since the function is continuous, we know they're zero lies between these two values between negative to negative one is the location of one of heart zeros. On the 2nd 1 2.347 But we'd say between two and three, and we can see the change in sign here between two and three. Those are the only to you part C. Ross of maximum and minimum. So maximum is like a peak. We have one of them here and about forward. We're just reporting the X value of this. So that's giving that location and valleys air the minimum. There are too low points here about negative 0.6 in about 1.7 or even 1.6 again, you'd be estimating off of your graph, then there has.

Her parents data graphics function. I want you to see the graph. That report is the decibels. Graphing calculator. Once you're there, I want you to type the function as you see it. How to type of power like the power of five me keep had in the A to the B button gets you into the exponents positions of a type five and right arrow to get out of it. And then you can finish typing in the rest of the function. Be very careful, not make a typo. Yeah, Once the functions and you can hide the key pad, you can drag the function around. You consume inter out. In this case, we want to zoom out a bit. And if your job is to put this onto paper, you can see how this function behaves. But you want some actual points to plot to help guide your graph so quick that well on the table and, um, I think we should at least see X values. They go up into five. So when you hit and turtle automatically populate right and pick a handful like between negative one and positive four are nice points to plot on a coordinate plain and then connect. So that's your graph. Now we want to focus on the zeros of the function for party zeros of this function are when the function crosses the X axis. That is when the function the output zero so visually when it crosses that when we know we have one and I see 12345 of them. Now, if you were to be just using what you put on paper, you can tell exactly where it is like this negative one point to a nine, so you'd have to ask to me. So we're just gonna report the integers that they're in between like that when we would say is between X equals negative two and X equals one. So that happened between negative two and negative one. Mr. The rest will write it out, but it also happens between negative one and zero between zero and one. Uh, between two and three in between four and five Now, you can also use your table of values for this notice when the output changes from a negative to a positive dysfunctions continuous between the negative and positive lives in zero. So between negative to negative one between negative one and zero between zero and one between two and three in between four and five. All right, so there were five of them here. That's right. The Moldow said between negative to negative one. Also between negative one and zero between zero and between two. And three in between four and five. Okay. Artsy relative Maxwell in minimum. Let's start with the relative maximum. These are your peaks. So, what's happened? A little hills were 12 of them. It happened That about negative one in about to. You can estimate, though. And using the graph that you spotted, you see it more like a negative 1.1 on the negative. All right, 2.1. Come. Extraction being negative. It should be positive race that you are estimating here. And the minimum there are two of those. It's about 0.1. About three points have been the X quarter for that. Okay. And you are Ask me so you can be slightly off. Here are meeting from your craft

For her. A. I want you to see the graph that we're gonna create in decimals. Graphing calculator, that the function. As you see it, open the keypad in order to get to the explosion. That's a to B. I don't allow you to type, for instance, like power four, then right arrow to get out of it. There's also a squared button. You type you you wish to once your function in is that you see your God, maybe two with this arc to coordinate. Graph paper thin out So you see the behavior of the function. But when you're transferring this a paper that we'll choose table. So you have nice points to plot like negative 2 to 42. That's not very pleasant. Negative 1 65 depending on your scale. 061 negative 1 to 2. Very easy. If you just keeping inter, we will keep populating. All right, so take a handful of these points to plot on paper. Connect them with this move. Continuous curves. Right. That's the graph for part of you were estimating zeros. Now, with dust, most you can see what this euros are exactly. They are where the function process The X axis. There are 1234 of them. But if you were just referring to what you draft on paper, we're just gonna estimated hits Andrews at thes euros or between. You can also use the table of values notice. These are all positive outputs, and then it switches to negative between zero and one. That means there is a zero between and exported of zero and want somewhere in between there I'm the next one between one and two because between one and two we switch signs. And again, this is continuous waste which signs we go through a zero. Okay, the 3rd 1 Here's the 3rd 1 It's between two and three between two and three. Switches from positive to negative. 2.6 is between two and three. Right, So between X equals two and X equals three in the 4th 1 is at 4.7. But you wouldn't see that on your paper. You would see between four and five because the outputs go from negative. And as our 4th 1 between four in five in part C, first relative maximum, um, there little peaks. And there's only one here and it happens at X equals two. We want to report the X value, the location in the relative minimum, my little valleys with the function Bottoms out and this happens in two locations. Um wanted it. Wait 75 another at four. And I will say to the nearest 10th. That's at about X equals 0.8 and next equals four you have.


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