in-the-following-exercises-solve-the-given-maximum-and-minimum-problems-in-example-3-change-1600-mat

Question

In the following exercises, solve the given maximum and minimum problems.
In Example $3,$ change $1600 \mathrm{ft}$ to $2400 \mathrm{ft}$ and then proceed.

Mike Gaerlan · Accepted Answer

All right. So when this problem, we&#x27;re trying to minimize the, um, dimension or the amount of material, which is the amount of fencing we need. So we&#x27;re trying to minimize the perimeter, which is equal to two length plus two with Pierre, right, and were given that the area has to fit a total of 400 feet, so length, times with must be 400. So to roost, reduce the sounds of just one variable. We can set one of these between variables to another using this form form or this equation here. So, for example, we can sit well, we can set link to equal to 400 or sorry, uh, this should be 1600 1600 so this will become 1600 divided by a W so we can plug that here into our, um, into our perimeter. So that becomes 3200 divided by the width, plus two times the with is our perimeter, and we&#x27;re trying to minimize this. So to minimize we take the derivative said it equal to zero. So the derivative here is going to be negative. 3200 divided by W squared plus two is equal to zero. Okay, so solving groups solving for solving for zero or sorrow, sorrow solving for W we get that 3200 over w squared is equal to two. Cross multiply. You get that w squared is equal to 1600. Or that w is equal to 400. Okay, so we have our with an onion, so this should be, um, in feet, 400 feet here. Okay. Now our length is going to be 1600 divided by 400 or we get that. Our link is also going to be 400 feet. All right, so we have finished our problem.

Prathan Jarupoonphol · Answer

this video, we are asked to fi the mess omen off the function if x squared minus y square when restrict to this graph. So first be get the function. Why as restriction curve here. And we are looking at there. Grady in the equation great in F equals Landa Times Square. The gnocchi I have calculated out is very simple. Just Polina meals. So we comparing the coefficient of X coordinate, we will get the system off questions asked to follow. So the first coordinate give Lambda equals two eggs. The 2nd 1 give Linda sequel miners. Why would three right? So this too combined means why yes, minus six eggs at the point of contact. So we will put this in our restriction function. Here we have eggs plus six time minus six is minus 36. Case equals four. So it turns out ex ese for over miners. 35. Okay, so why would I put my nest daughter minus four over 35. So why is minus six time eggs? So is 24 is become plus now, 24 were 35 malfunction if now has extreme um, at these Well, you are X and wife, so we put them in. But before that, we don&#x27;t want to square these two fractions so we can simplify it a little By breaking it like this. The first term between the over 35 the second term will be minus who in the end, and luckily, this too can be reduced efficiently. So is four over seven because we divide by five times minus four or five because we divided by seven. This gave minus 16 over 35 this is an extra month. But is it me? No, Max, will you? You can randomly shoes x y that satisfied is rest fiction function. I wish youse four and a zero. Yeah, on and put them in function if we will get 16 right, which is clearly more than the extra mommy just fired. So it turns out this is minimum. So we go back and answer if mean he is minus 16 over 35 and you may ask, What about maximum here? In this case, we don&#x27;t have maximum because the grab the restoration here can go on forever. We can put, uh, we can always put why as four minus x over six right? Yes. So no, mate, huh? No help. What? Value off XV one we can put. Why ask this one and sorry? Why? Square will be, uh, ex choir over six. Plus something we don&#x27;t catch. The important thing is that the first term is Esquire over. Sorry that this is not six. When is like this? If you plot this in function, if you always the first term, we always be 35 over 36 off x square, right? Plus some stuff. Now I do it like this because when x get really large, the first term will be the only one dictating how How big the well. Oh, is because the letter term would be my ex power by one or x power by Ciro. And they are insignificant compared to X square. So I just want to show you that here with this condition, X can be whatever like 10 to the 100 if you want, and we can find why to match that. And the function is gonna go to to that skill wishes really be. But it can keep growing. So no Max in this point. And that is the answer. Thank you.

Prathan Jarupoonphol · Answer

deal. We are going to Fi Min and Maxwell you off this function if x y equals x squared times. Why, when restaurant with this Kurt, these X squared plus y two y squared equals six. So first thing first we have to look at the credit equation. Grady in off f equals great and g times some constant. This constant is the background question. Uh, so the way to fight radiant is we five. They&#x27;re a team, but off the function by ish, office free, variable and attached them to these You need better, like a coordinate victor. And on this I is de so I&#x27;m not gonna go away. And the point is, when we have this equation, the well ooh, attached to each chord in it has to be the same for for them to be equals right. So we will have you have to x y equals two eggs than that from a cord in it. And x square equals for while under from J J cord in it. And we will use these to equation together to fi. Yeah, well, you off x and y. And here we go. We first we have you say it, uh, then that you close to why, Right? We pluck this in. We have X square, my nest for why square equals zero. That is to say, X is plus minus two. Why? And here we can eliminate one. Aagh! Wearable from the equation. So restriction equation is a square plus two White Square equals six. We put put this in to eliminate eggs. We&#x27;re gonna get Why four squared. Plus sorry for y squared. Plus two White Square. It&#x27;s six. This is six White Square, right, So it means wise quays. One whyy is actually just a plus, minus one. And so, from from this again, X will be plus minus two. And now we have weather world possible X and y like full cases. We have to 51 mean and max off this expression to use. And you&#x27;re gonna see that X square, No video. What science is gonna be full always. Right. So what changed is why use plus or minus and here we have it. Max would be full. Mean would be minus four. You want to check it? This is correct. You plug this in plot this Indy restriction equation, and if you do like some other question and you plug this back and it doesn&#x27;t satisfy the equation. Then something is wrong. But in these cases, correct is really simple. Okay, that is the answer. Thank you.

Amrita Bhasin · Answer

this question asks us to approximate local minima and local maximum. We know her graph. Look, a little something like this with the point down here, ABS Negative. 0.63 negative. 0.472 You know the lowest point or global minimum is negative. 0.472 approximately.

Amrita Bhasin · Answer

this question asks us to approximate local minimum maximum or global minimum maximum. We know we have two X cubed, minus three X minus one. Using a graphing calculator to graft this. You should end up with the function that looks something like this. As you can see over here, we know we have a couple of points. You know, we haven&#x27;t intercept of 1.33 so I won&#x27;t. 0.36 Sex, comma zero. And then down here, we have 0.707 common negative. 2.414 and negative. Zero point 366 Prom A zero. Okay, What this tells us is that we know we&#x27;re going to be looking at the local minimum. Is your 0.707 negative. 2.414 and the local maximum. Right over here. 1.366 Mama&#x27;s here.

Problem

In the following exercises, solve the given maxim…

Problem 1 Easy Difficulty

In the following exercises, solve the given maximum and minimum problems.
In Example $3,$ change $1600 \mathrm{ft}$ to $2400 \mathrm{ft}$ and then proceed.

Answer

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