find-an-equation-of-the-tangent-line-to-the-curve-at-the-given-point-y-ln-x2-3x-1-3-0

Question

Find an equation of the tangent line to the curve at the given point.

$ y = \ln (x^2 - 3x + 1), (3, 0) $

Doruk Isik · Accepted Answer

in this problem, we&#x27;re gonna function while end up or arrested for questioning potential lined up through this point. The first question Centauri will be a 41 minus Warner is equal to There were 10 alike, even for extra times. X months. That&#x27;s not so. Now we personally for their dysfunction. What, since given function is natural law of extreme earth tricks, What&#x27;s for charity will be won over experiments Tree. It&#x27;s possible in love by your function in this is that is too explains three. So we need to do, you know, like they ever took that given points. So one exit three that would be more over nine Bryce. Nine swarm of two times, three months free nine will go where you find over too to be three. So we&#x27;re just gonna think is there were two men at play here and find you clich? As for 103 times exports free performance. We see that the equation is that wise 3000 ones

Anthony Han · Answer

So here we give an example of specific cubic function, let&#x27;s say it has this sort of a shape and were given information that we&#x27;re interested in the tangent line at the point. Let&#x27;s call the point here 2:03. So the tangent line would be why I minus the value of the function at a certain point. So why minus Y. Of two would be equivalent to the derivative of the function at the X value times x minus The certain x value or interest in which the X -2. So this will give the equation of the tangent line. So we have function Y equals execute minus three X plus one. And if we take the derivative of this this would be equivalent to three X squared minus three. If we evaluate the derivative at the point X equals two, So be four times maybe four times 3, 12, 12 -3 is nine. So we&#x27;ll be getting information. This would be rewriting this would be AY -3 Equals nine times x -2. And this means that Y equals nine x minus 18 plus three, which B nine x minus 15. And this is our final answer.

Madi Sousa · Answer

in this problem, we have to find the equation for the tangent line to a curve and specifically were given a curve that is defined by a log rhythmic function. So we have the function. Why equals X square times the natural log of X and what we need to do before we confined the tangent line is find my prime. Well, how do we do that? We&#x27;re going to have to apply the product rule. So why Prime would be equal to d X square dx times the national log of X plus x squared times d natural log of X over d x So when you do that, we simplify just a little bit. We get why prime equals two x times the natural log of X plus x So we have the derivative. But we want to know the equation for the tangent line. So what do we have to do now? We need the slope of our tangent line at the point that we&#x27;re told in the problem 10 so we can plug in our X value into y prime. So why prime would be equal to two times one times the natural log of one plus one, so we would get zero plus one, which equals one. And now we confined the tangent line very easily. We have this form. Why? Minus why not equals M times X minus X not. And then we could just plug in the X and Y coordinates from our point, so we would have y minus zero equals one times X minus one, and then we can simplify to get the tangent line equals Why equal toe X negative one x minus one. Excuse me. So I hope that this problem helped you understand how we can find the tangent line to a curb using differentiation, specifically finding the derivative of a of a logarithmic function.

Heather Zimmers · Answer

we&#x27;re going to find the equation of the tangent line to the curve y equals square root one plus X cubed at the 10.23 The slope of the tangent line will be the derivative at that point. So let&#x27;s start by finding the derivative. And I&#x27;m going to rewrite why, as one plus X cubed to the 1/2 power. And so then I can use the chain rule, starting with the derivative of the 1/2 power function. Bring down the 1/2 and raise one plus X cubed to the negative 1/2 power. And then we multiply that by the derivative of the inside, the derivative of one plus x cubed is three x squared. Now we&#x27;re evaluating this derivative at X equals two. We could simplify first, or we could substitute the two in first and simplify after. So that&#x27;s what I&#x27;m going to do. So 1/2 times one plus two cubed to the negative 1/2 times three times two squared. Okay, so this gives us 1/2 times nine to the negative 1/2 times 12 and nine to the negative. 1/2 is 1/3 so we have 1/2 times 1/3 times 12 So that is just too. So are slope is, too. Now we can use point slope form. Why minus y one equals m times X minus X one. To find the equation of the line where the point x one y one is 23 So we have why minus three equals air slope to times the quantity X minus two and we can simplify that and we&#x27;ll have the equation of the line. So let&#x27;s distribute the two. So why minus three equals two X minus four and then at three to both sides and we have y equals two x minus one.

Clarissa Noh · Answer

he had clear. So when you right here. So the tangent line at point. A bee has slope m equals D Y over DX access equal to a and the form of the equation we use is gonna be point slope, which is why minus B equals m times X minus a. So we have m, which is our derivative d over d x of two X cubed minus X square plus two when X is equal to one and this gives for so the line equation is why minus three is equal to four terms X minus one, which is equal to four x minus one.

Gregory Higby · 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.

Doruk Isik · Answer

on the question to the tension lines. So here first we take, the derivative is excluded by Cheryl with numerator Will bees on the roof he offers a denominator. Here&#x27;s to X minus three. No Employment Street together. Slow snow Bobby played three six months three nine minus nine plus one, which is three over one, which is three. And therefore, by knowing the slope ends appoint you used poison or form. Not Rosa the equations of lines. Why my zero? Because slope on X minus three, it&#x27;s simply five further.

Doruk Isik · Answer

and this problem. We&#x27;re finding the equation for the tangent line to a curve. Specifically, the function of that curve is log rhythmic, and we&#x27;re also given a point at which we have to find the tangent line. So the function were given is why equals the natural log of X squared minus three x plus one. So the first thing that we need to do before we can find the tangent line is find the derivative. So we need Y prime. How are we going to do that? We have to use training role. So why prime would be equal to one over X squared minus three x plus one times two X minus three. Now, if you&#x27;re confused about that, basically what you do with chain rule because we know the derivative of the natural log is one over X, so we would have one over X. But in this case, it&#x27;s this entire input and then we&#x27;ll multiply by the derivative of that input. And then we can simplify Why? Prime to be two X minus three over X squared minus three X plus one. So we have the derivatives, but we need the slope of the tangent mind at the 0.30 so we can find why, prime of three, why crime of three would be equal to sticks minus 3/9 minus nine plus one so it would simplify to three. And now we&#x27;re very close to finding the equation for a tangent line. We can use this point slope form why, minus why not equals m times X minus x dot So we can just plug in the point that were given why my zero equals three times X minus three. So you can essentially write the tangent line in this form or you can simplify it in point in slope form and we would have Why equals to reacts minus nine. So either way, they both mean the same thing. These air both the equation for the tangent line to our curve at that point. So I hope that this problem helped you understand a little bit more about how we confined the equation for a tangent line, using our knowledge of differentiation of logarithmic functions and then plugging in the point in our, um, coordinate plain to find the overall tangent line

Problem

Find an equation of the tangent line to the curve…

Problem 33 Easy Difficulty

Find an equation of the tangent line to the curve at the given point.

$ y = \ln (x^2 - 3x + 1), (3, 0) $

Answer

$y-0=3(x-3)$

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$y-0=3(x-3)$

Calculus

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Kayleah T.

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James Stewart

Calculus