a-find-an-equation-of-the-line-tangent-to-the-given-curve-at-a-b-use-a-graphing-utility-to-graph-the

Question

a. Find an equation of the line tangent to the given curve at a.
b. Use a graphing utility to graph the curve and the tangent line on the same set of axes.
$$y=-3 x^{2}+2 ; a=1$$

Subhadeepta Sahoo · Accepted Answer

they cost another 10 genders given us why minus zero Issa quarto Best tuxedo X minus X zero But zero invited on the points on that tangent That s the car. And at best, tuxedo the strobe The tension between nothing but negativity. So he had perfected bitterness My next three x squared plus two. Let&#x27;s do so That&#x27;s extra deep but that you have to know Devil function minus six x only now that they do to the function it extra dough with excellent given as one minus 6 to 1 They called to Linus six not to find the point of ice. You know, we have I theoretical f of X ido you call the minor strain toe one squared plus two and white. It&#x27;ll regardless minus one. But they Christian on the pendant will be live minus Why do you know it is minus one? If your toe and this texutil in minus six Unwto explain us extra This one something we did Y plus one. It&#x27;s 1/4 minus 66 Bless six. Finally, we got the answer. This why is it to minus 66? Let&#x27;s fight should take with another contingent

Alex Roush · Answer

Okay, so the question is asking us to find the equation of the line tangent to this function. It&#x27;s a Freddie graph. Any function f of X, the tangent line at a point X equals a is going to be the line. It just touches it at that one point. So the slope at a point we&#x27;ve discovered is the derivative. And the only other thing we need for the equation line is the whiners. It&#x27;s the first thing I need is to find the slope of that line. And to do that, I&#x27;m gonna take White prime. So this is gonna be the caution role. Why? Prime is gonna thus equal the bottom function tends the derivative of the top minus the top function attends the derivative of the bottom all over the bottom functions squared. Okay. And at this point, it doesn&#x27;t even matter if you simplify this because I want the slope at a specific point at X equals one. So you can just plug that in for X, okay? And you&#x27;re gonna get three times one minus one, which is to times four minus two times three all over three minus one. Sward casements eight minus 6/4, which is gonna be 1/2. So that&#x27;s the slope of my line. Now the only other thing we need is the y intercept. And there are two ways of going about finding the Y intercept. The first way is the hypothetically say that put it in Point Slope form Michael&#x27;s and X Plus B Plug in the value we just got for the slope, okay? And then utilize some sort of x and y. Or you can use Point Slope form, which says that for any specific point x one y one, the equation of the line will be why minus y one equals M times X minus X one are their way. That&#x27;s going to require a specific point on that graph. And there&#x27;s actually only one guaranteed point that we know is both on that line in the function. And that&#x27;s the point of tendency. So we&#x27;re gonna take this this X equals one, and we&#x27;re gonna find out what the Y value that corresponds to this point is so I&#x27;m actually just going to take why of one in this original function to get two times one squared over three times one minus one, which is just gonna be one. So this tells me that a point on the line is has an X coordinate of one by the problem and plugging this into our function we got one was the Y value as well. So now we have a slope and we have a point on the line so we can now use point slope. So this says that why minus y one which is going to be one equals the slope tends ax minus x one where one common one is our point. So now simplifying this just a little more we get, why equals 1/2 X and this is gonna be minus 1/2 plus one plus one came from from adding one to both sides. Okay, the final equation of this line is going to be Why equals 1/2 X and then we have ah, negative 1/2 plus one, which is a positive 1/2. Okay, So the second part of the problem asked us to use some sort of graphing software in order to illustrate what I just showed here in general. OK, so we&#x27;re gonna actually graft this on decimus. It&#x27;s one of my favorite graphing utilities because it&#x27;s free and online. Okay, so we&#x27;re gonna take y equals two x squared, divided by what was it? Three X plus one, I think X minus one. Excuse me. Uh, OK, so that&#x27;s our original function out of function that we got this tangent line should only touch it at one point. OK, so that was like walls. Ah, half X plus 1/2. As you can see, this 0.1 comma one is a point of tendency that both this graph in the line haven&#x27;t come, okay?

Amy Jiang · Answer

declaring an equation Tangent line given are, which is why at a party today. So we need to find our points X com ally and our slope, which you&#x27;ll find taking Rto derivative. And then we&#x27;ll put that into our point slope form, which is why I, minus Phi one, is equal to and the Times expertise X one to find the equation of our tangent line. So it&#x27;s fucking is it? Which one? Three minutes? One. That&#x27;s two people to one so we get the points in common one. Now let&#x27;s take the derivative from a D. Why over the X that&#x27;s equal to we&#x27;ll use our quotient. Also derivative of to access. If you go to times three x minus one and then minus derivative of three X minus one. That&#x27;s the three times two X over three x minus one squared. Okay, so we get six x my still minus it. Six x over three exports once worth used to cancel well off with and like to over three X minus one. Squared for a slow we&#x27;re playing an acceptable to want to find determinative. At that point, we&#x27;re three minus one that&#x27;s equal to two square too much for so are derivative or a slow busy. Which one house? Let&#x27;s put that into our equation. So why might each one is equal to never have, uh And then, um, that&#x27;s minus one. And I will add one to both sides to get y is equal to negative 1/2 acts and plus 1/2. And this is our equation of our times, that money.

Anna Waldram · Answer

we want to find the equation of the tangent line at point A when a equals two. So, in order to find the equation of the tangent line, will first want to find the slope of the tangent line, which we know weaken dio using the derivative. So first will find the General Dilip derivative of why, and then we&#x27;ll plug in at 0.2. So the general derivative of why gives us three X squared minus eight X plus two. Now we can plug in our point to to find it exactly that point. And when we do that computation, we get negative, too. And now this negative two gives us thes slope or which we call em of our attendant Lee. Now, to find the rest of the part of the equation, we need the intercept. The why intercept. So I like to do this by taking Why equals X Plus B and plugging in a Y and an X value so that we consult for B in order to do this. We know exactly one coordinate point that is going to be on both the tangent line that we&#x27;re trying to find, and it&#x27;s where it touches the curves that we begin with. So we will want to use point to. And when you plug in to to the original curve we see the thing why value is negative. Five. So we put that and why is native five X is to? So we plug all that in our m is negative two. So we get negative. Five equals native, two times two plus B and we get our be equaling negative one. Now we have an M and A B, so we can construct the equation. Y equals negative two x minus one. And that is part A, the equation for the tender line. Now, for Part B, it wants us to simply graph on a graphing calculator or something similar both the original curve and this tangent line at 0.2. So we&#x27;ll want to club in this equation and then the equation that we just found in part A. And when we do that, this is the graph that we come up with, and that&#x27;s is Burpee

Linh Vu · Answer

in this question. One. Even the function gwihn in coaching the ministry X squared plus two. And then I go to one here. You need to find a attention online force. We need to find a wife prime. And then we will have. This will be the finest three X Square cramp list to cram and then the constant Here we can be in our sign and forget a month. Three x square Prem plus the reveal a constant here, equal to zero therefore Bella&#x27;s area and finally found a power room in riveting. Can you cut you that in terms and spot and my was going and for indigenous language your ministry times do expert to minus one and they were getting put u minus six x So this women a white graham. Therefore, from here we can find a slow You go to them and they go to the UAE prime and available a go to one year one and we get a minus six times one and they put him under six. We know that done to life and as a formula, why includes your m express be and four million quite cultural Brenda six experts be defined be. We know that. And the ex coach you won, they would have a 11 We called you Ministry Temp&#x27;s one squared plus two and include tremendous one. Therefore can probably break it into here. And then we get the what? Why would you mind ask one in called U minus six times one. Let&#x27;s big for being a deacon. Judah, Uh, six months. Women be five. And from here again, the worry. Tension lighting culture minus six. Thanks plus five.

Linh Vu · Answer

in his questions, like even the function one. Because you&#x27;re the expert. Three minutes for X Square plus two x minus one and they were given any with you two. And first immunity find will be the white Bram, and we use a formula for the power over here. Conduct expelled in the riveting in coach ilda Intense X off and minus warm. And then we should get a grip. Kremikovtzi took three next about three minutes. One. But it&#x27;s fun times to expel under two minutes. One. Let&#x27;s chill times is only about one here, x one minus one and for the constant again zero. Then we have a one primary culture that three X squared minus eight X plus two x plus two Only this women went prim and now, given that I could teach you have the strong think of your aim is good. You, my Graham to you were getting close to the three attempts to square minus any times two plus two and we get Nico June here we have designed being the trail minus 16 plus two. So we&#x27;re getting coaching the miners to, and we know that until light it has a formal why go tuna and express big? Therefore, we again why Eagle Jr minus two experts Be now even the ankle to to, you know, going to include you that to about three minus four times to square does to attempts to minus one Doing it includes eight miners. There&#x27;s only basics 10 plus for minus one. Then we get this Junior Echo Children bonus far plus minus one to minus five and then we will have Doesn&#x27;t why therefore we have tremendous five echo to ministerial times two plus B from him again be go to nearly halve include tremendous one and then we get the worried Kikuchi Divergence two x minus one

Problem

a. Find an equation of the line tangent to the gi…

Problem 59 Hard Difficulty

a. Find an equation of the line tangent to the given curve at a.
b. Use a graphing utility to graph the curve and the tangent line on the same set of axes.
$$y=-3 x^{2}+2 ; a=1$$

Answer

a. y = -6x + 5 $\\$
b) graph

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a. y = -6x + 5 $\\$b) graph

Calculus Early Transcendentals

Catherine R.

Anna Marie V.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

William Briggs, Lyle Cochran, Bernard GilletCalculus Early Transcendentals

Catherine R.

Anna Marie V.

Michael J.

Joseph L.

a. y = -6x + 5 $\\$
b) graph

William Briggs, Lyle Cochran, Bernard Gillet

Calculus Early Transcendentals