find-an-equation-for-the-tangent-line-to-the-graph-at-the-specified-value-of-x-yleftx-frac1xright3-x

Question

Find an equation for the tangent line to the graph at the specified value of $x .$
$$
y=\left(x-\frac{1}{x}\right)^{3}, x=2
$$

Gregory Higby · Accepted Answer

eso these tangent line problems. You need to know your ex cornett, which they tell you. I mean called x one. Now you need to find your wife. Cornet, you need to find your slope. Um which the slope is the derivative when X equals two and a reason why you need this is in point slope form. Um, written like this I prefer this form. All you have to do is fill in the blanks. What&#x27;s your M? What&#x27;s your ex one with your Why one? Well, we already know the X one. We also know the equation they tell you is X minus one over X, uh, cubed. Well, if we plug to into this problem here and here, we get to minus one half, which I hope you know already is three halves. Well, if you cube that, you&#x27;ll get three times. Three times three is 27/8. I just found the y coordinate. And now what we need is attributed of this. That&#x27;s where the changeable comes into play and why they&#x27;re doing it here, where you bring the three in front X minus one over X is now to the second power times that by ah, the derivative of the inside. Uh, which is one minus. Well, this is excellent at your first power. So you bring the native first in front X to the name of second power because you subtract one from that, you write it like that double check my math. What&#x27;s nice? Those we plugged in to earlier, like, into this piece. So it&#x27;s very similar because we did two minus one half, which is three halves. But now we&#x27;re squaring that piece times one plus 1/4 cause two squared is four. And that&#x27;s five force. So this is how I would do this, um, three times, three times three, cause you have to square it is 27 times five. I need a calculator for, um, so you get 135 in the numerator and in the done nomine area of two times to just four times for 16. So when we go to write our answer, I just found the slope under 35 16 x minus your x coordinate, plus your y coordinate. There&#x27;s 27 8 Now some teachers will make you changes to slope intercept form. I am not one of those, but you can easily if you want to distribute that and combine like terms and use a calculator to get there.

Taylor Shimono · Answer

so for this problem because we&#x27;re finding the equation of our tangent line to our graph here. And we can go ahead and start with a stating our knowledge that when we find the derivative, we are finding the slope of the tangent line at one specific point. I&#x27;m so essentially are slope of our tangent line. It&#x27;s just going to be the derivative of this at X is equal to one. I&#x27;m so the derivative of three X squared. Using our power rule is will move that to to the front is six x minus The derivative of X is just one I&#x27;m so since we know that this is that X is equal to one, we&#x27;re just going to plug in one for X here and find that are slope is equal to five. And lastly, to figure out the equation of our attention line, we&#x27;re going to need to find one point on our graph. So the easiest is just going to be plugging in X is equal to one and solving for why so we know that wise equal to three times one squared minus X is one. So this is dressed equal to you too I was. That tells us that we have the 0.12 on our graph. And so using our slope and our point, we can go ahead and find our equation of our tangent line in point slope form, which is why minus whenever the white corner of our point is, which is to is equal to our slope, which is five times x minus the X coordinate over plate. Um and so from here we have the point slope equation of our tangent line to our graph at X is equal to

Gregory Higby · Answer

eso Since we&#x27;re given this equation X over square root of one minus x squared, there&#x27;s three things you need to know. Um, the first is what they give you. What X is you need to figure out why is, well, if you plug zero into this, you have zero divided by one. Well, zero divided by 10 Um, and then you need to figure out with Slope is when X equals zero. And the reason why that is what you need to know is because I&#x27;m using point slope form as like writing it this way. Um, and that x minus your X coordinates, plus your Y coordinates. Um, whatever this answer is is going to replace the slope because that&#x27;s what the slope derivative will find you. The slope at a point. And we already figured out earlier that the X coordinate a zero in the white corner zero. So just you know that so what, you need todo Let&#x27;s figure out the derivative. This is definitely a quotient. Rule within a chain ruler are, however, are saying it might sound wrong. The driven over the top is one. You leave the bottom alone, minus you take the derivative of the bottom, which is one half to the negative one half power. You leave the function alone inside times the drift of the inside, which is negative. So I changed it. Two plus two x and then don&#x27;t forget to leave the top along Times X all over the denominator squared so knows the square root will cancel out with square So I just didn&#x27;t write that. So now what we need it was plugging zero in for all these excess. Well, that actually makes all this work I did earlier move because if x 00 times, anything is gonna be zero, Um, but what we end up with is one minus zero on top square to one is one over this zero squared 01 minus zero is one. So the slope is one. I&#x27;m just filling this in. Although plugging in zeros there the equation of change a line just one x It&#x27;s a like als X What we&#x27;re looking for

Vikash Ranjan · Answer

Yeah, we have been given. It affects iwas. It&#x27;s minus wanted The power of three. You&#x27;re a fool. Your best X is equal. Do three x minus. Want to the power off? Two into one. This is equal to three X minus one. What is what now we have to find if off. Whoa. This is given as to minus one. The power of cream this is equal to one on X is equal to X. One is equal to two on. And if that&#x27;s too is equal to train to two minus one to the power off. Two is equal to a tree. Yeah. Four, No equation off. Tended line is given as why minus one is equal to X into extra minus X one. This is equal to y minus one. And that is equal. Do three. He drinks a minus two. So it becomes why wise three X minus six plus one. This is equal. Do three X minus five. So here. Why? Zeke was treats minus five. So this is the ignition off the Kenyan plan. It doesn&#x27;t answer given from

Taylor Shimono · Answer

So for this problem in order to find the equation of our tangent line. Um, what we&#x27;re going to need is we&#x27;re going to need one point, which is going to be at X is equal C three and we&#x27;re also going to need to know the slope of our line so we can go out and start by finding our point. So we know that we want our point to include X is equal to three. So we&#x27;re just going to plug it into our equation here and sell for why I&#x27;m still going to do that. We get wise equal to three cute minus three times three. So that&#x27;s going to be 27 minus nine. So why is equal to 18? Which means that our point here is going to be 3 18 I&#x27;m And then from here, we&#x27;re going to be able to find the slope of our tangent line. I&#x27;m by finally derivative. So we know that why prime of X, which is our derivative by using the power, will hear the derivative of X cubed is three x squared minus the derivative of three exes. Three. I&#x27;m so since we know that we want this to be at the point where X is equal to three. We&#x27;re going to you find why, prime of three and this is equal to three times three squared minus three. I&#x27;m so again 20 v 27 Ministry, which is 24 so we can go ahead and use our 0.3 18 in our slope of 24 in the point slope form of a line. I&#x27;m to tell us that the equation over a line is going to be why minus why one. She&#x27;s why once 18 is equal to our slope of 24 times x minus X one, which is three.

Gregory Higby · Answer

eso these tangent line problems you typically need the X coordinate Negative pi over two. It typically need to like, well, you definitely the white core. And you need the slope. While the slope is always the derivative at a point, Um, this is usually the notation that we write it as And the reason why these are the things you need to know is I like to write my answers and point slope form expanse your X coordinate, plus your wide corners. So maybe best fire like X one y one. Because we&#x27;re you know, this x coordinate. Um, and they also tell you what the equation is, which is the seeking cubed of pirate two minus x. Um, So the first thing I would do is plug in pi over two into this problem. Well, as you do that, um, and be pirate two plus high over to, um, which is two Beira, too. So this is basically the same thing is I would write it this way. One of her co sign cubed of pie. Um well is you&#x27;re looking in a circle Pi is over here. Uh, that&#x27;s the order. Para native 10 So CO sign a pious negative one when you cubit is still negative on one over naked one is negative one. So when I get to this point, you know we&#x27;re gonna have a plus neighbor on r minus one here. And the other thing you need to do then is find the derivative. Well, that&#x27;s definitely a chain roll. It&#x27;s actually change role inside of a chain role. But we&#x27;ll get to that. You bring the three in front. It&#x27;s now seeking squared of pirate two minus X. They had to take the drift of of seeking, which is seeking tangents will make the seeking cubed tangent of pirate to money. Sex. I kind of ruined things for us times the drift over the inside, which is negative one. So I&#x27;m just going to take a negative for the reason I say this actually ruined stuff for you is right. This piece right here because tangent is signed over co sign Well, if signing zero over negative one will zero divided by anything is still zero. I don&#x27;t care what this is. I don&#x27;t care. This is zero times something times something is still zero. So the drift of actually call zero. So the long answer is, if you want to your right. Like will&#x27;s zero x minus the X coordinate. So plus pirate too. Plus your white corner, which is negative one. But what? Zero times? Anything at zero. No need to write That you know is right. The horse on the line y equals. Think of one is a tangelo on here?

Problem

Find an equation for the tangent line to the grap…

Problem 46 Hard Difficulty

Find an equation for the tangent line to the graph at the specified value of $x .$
$$
y=\left(x-\frac{1}{x}\right)^{3}, x=2
$$

Answer

$1135 x+16 y+216=0$

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Calculus Early Transcendentals

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$1135 x+16 y+216=0$

Calculus Early Transcendentals

Anna Marie V.

Samuel H.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

Anna Marie V.

Samuel H.

Michael J.

Joseph L.

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals