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What curve do the parametric equations X = e y = e2t represent? Find the slope of the tangent line to this curve at the point (3, 9). Find the concavity of the curv...

Question

What curve do the parametric equations X = e y = e2t represent? Find the slope of the tangent line to this curve at the point (3, 9). Find the concavity of the curve at this point.

What curve do the parametric equations X = e y = e2t represent? Find the slope of the tangent line to this curve at the point (3, 9). Find the concavity of the curve at this point.



Answers

Find the tangent line(s) to the curve $y=x^{3}-9 x$ through the point $(1,-9) .$

We're giving it Council of graph. Why do you go? Excuse minus nine. We can put the slope, then out. Business dependent line, which is passing through one. Come on. My last name. But this is no longer than that. So us will compute that very Betty Bob. About what? Why? With respect exit will deliver People quite expect to eggs People do Here. The X squared minus name using the power rule up deliberately. I don't know derivative. While I inspect it gives us a look off that 10 yard line. So we can I in medical to TV. Excess squared. Minus name Reginal. Slow attendant lining. Why? Minus why you want divided by X minus X one. Did you call PD Extra square? Main ethnic Were example More why you wanted one. Come on, minus So like. Here they get minus nine X minus one Vehicle idiot to square minus name now, But like in the value of white value up. Why x Q minus nine. Well, right here, X Q minus 98 Minus minus. Bless you. Last night you I did right X minus one will do periods per square minute. Normally like most side by X minus one. Then you will get a X cubed minus nine x last night. Physical do X minus one in do Petey Petey X squared minus name. Like keeping X squared minus x Q minus nine x listening. Nor multiply this one. Then you will get here TV X Q minus nine X minus. TV excess wet, Lessening now take all. Come right inside here. Then it will get their TV X Q minus nine X minus 50 X squared. Last name. Now, if you'll excuse in the plus. So you right here minus X cubed plus nine x minus, not cancel this one. Also cancel nine. Expert. Now we'll get here T x Q minus X Swede Who X Q My next. Pity Exit square. Now we can act like that to excuse. Mind that, Terry. Excess square physical todo Now take the common x square from the these these students. Then they get excess quack, tickle toe to x monetary Little good deed. Oh, now we have a new picture. So I don't exist. Critical. Good. You Oh, who? X man. It's really difficult to get from here. The value of X zero and the from hair look exists. Three big toe. Now we have a rubella Joe Exhale. So we'll get a Jerusalem off them Given God. So you know of the this is gonna be TV exist where? Minus nine years. No plugging exit. Scalpel, Joe. Then it will get the Belo Snoopy Gideon du Jeu square minus nine to minus nine at X. It's going to you. So you can. I dead at exit sculpted you. No sloping minus nine you can capture. That is number 10 Usually, I don't know the formula for that. It is not attending my minutes. Were you in? It's a little came into X men. It's excellent. Were X one Y one Egypt, one comma minus. So the daily walk Why one is my last night here. Then they'll get pipe last night they do up Amy my last night X men and develop explanation one. No, you simplify this one. They get by Polis nine minus nine x less not suspect, both side nine. Then it'll get why ableto minus nine they should. The prospect of opinion line now will come to the griz Number 10 it like a physical anyway at excellently bedroom. Slob, he's here in new TV Bay to get up all this crab minus nine. From here we get nine. X squared is serious. Quite 99 tonight 27 on seven Bank. Who will get image ical You won't be seven by four minus nine. No, simplified This one. Then they will get minus nine Bite. Pull this. Look off that when you're lining minus nine My poor, they respond. Potentate lining by minus one vehicle came into X minus. Excellent. And then what? Why even eat minus name? So we'll get wiped last night and the value of a me enough man report in tow, X minus one thing No, simply fight this one. Then you will get my man four x my mask plus nine. Make food. No subject. Both said why? Then he'll get minus +94 eggs plus nine Big four minus night. No simplified This one. Then you will get a logical reminded nine made four x minus. Don't deceive inmate. Who? That I know. Thank you. So we'll get here to decrease in other then Middling

The questions is show that the tangent to the co. Why calls to seven X cubed plus 11 at point X equals C. Two, and X equals two minus towards parallel. For the government equation, slope of the tangent at x comma Y will be equal to the vibe, I d X equals to 21 2 X square. Now at the point x equals to two Slope of the tangent are 21 into two square equals 21 into four, which is 84. Now moving further, slope of the tangent is equal to 84. Since the slope of the two, tangents are equal, therefore the tangent of X equals to two and X equals two minus two are parallel to each other. Thank you.

Welcome to enumerate in the current problem. We are given Polynomial. Why is we called you three x cube minus nine eggs and then find this low bar the deliberative of the given polynomial and the point X. Musicals to work. So to do that first we have to find the derivative. So by taking derivative on both sides we have D D. X. Off three XQ -9 X. No D V T X. And then be three of D D X. X cube minus nine D D X. Of X. You can follow any Previous video of mind to find why this thing turns to one not just because of the implementation of the formula this but also with some numbers and tables. And that would that might clear up your idea or notion of this And I have used over the Newtons interpolation. So even if you don't find the previous video, you're always will come to learn about these topics because that will help you understand how derivatives work or how did Newton get the idea of this? So now this is nothing but mine X squared minus nine. So therefore the derivative at the point X is equal to one will be nine into one square minus nine, Which is 9 -9, which is zero. So at the point this at the point X is equal to one. This polynomial will have a graph of city. So let me tell you how this might look. A cubic uh, polynomial looks like this third degree when it is multiplied with three. It will be a little more open. So this will be the cubic point. Well. And since there is some linear uh function as well. So there will be a slide shift. But it will be somewhat like this instead of uh the this being the Y axis. Imagine this something of the sort it will be and you can see at X equals to one how it is becoming zero, there slope is becoming Yeah, same as that X axis. So I hope you couldn't understand the problem. Let me know if you have any doubt of this.

Parametric curve CFT where this tangent line has sloped M equals three. Okay well remember the slope of the tangent line is equal to the derivative of why with respect to X. Okay so your choices are you have two ways to do it? You can use equation six or you can try and eliminate the parameter and then take the drift of the regular way. Okay. Both of these are going to be hard to solve her T. So we want to just use equation six. It's the best way anyway. And it says if you're doing dy dx then you take the derivative of Y with respect to the parameter and then the derivative of X with respect to the parameter. So the derivative of Y. Three T squared minus six, the derivative of X 16 minus two. And they want to know when does that equal to 3? So let's make that 3/1 cross multiply and you get three T squared minus six equals 18 T -6. So three t square minus 18 t Plus six. Those go away equals zero Factor out of three T. So at T equals zero and T Equal six. So at the points in tangent equals three. At When T0 We're at 00 And when T is six were at we get stopped and calculate CF six is 636 times 308 -12. So yeah um 88 96 And then six cubed -6 squared. That's six square times 6 -1. That's 36 times 5 1 8, 210. So at the zero and the .96 to 10 Um the derivative is equal to three.


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