4

Find an equation of the tangent line at x=a Use graphing utility to graph the curve and the tangent Iine on the same set of axes_yex?_ 5x2 2x + 3;a=2The equation of...

Question

Find an equation of the tangent line at x=a Use graphing utility to graph the curve and the tangent Iine on the same set of axes_yex?_ 5x2 2x + 3;a=2The equation of the tangent line ata =2 is y=L b. Choose the correct graph below: All graphs are shown in a [ - 3,3,1] by [ - 20,20,5] window:

Find an equation of the tangent line at x=a Use graphing utility to graph the curve and the tangent Iine on the same set of axes_ yex?_ 5x2 2x + 3;a=2 The equation of the tangent line ata =2 is y=L b. Choose the correct graph below: All graphs are shown in a [ - 3,3,1] by [ - 20,20,5] window:



Answers

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. $$y=-3 x^{2}+2 ; a=1$$

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'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'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'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.

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'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're trying to find, and it'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'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's is Burpee

Okay, so the question is asking us to find the equation of the line tangent to this function. It'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've discovered is the derivative. And the only other thing we need for the equation line is the whiners. It's the first thing I need is to find the slope of that line. And to do that, I'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'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'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'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'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's going to require a specific point on that graph. And there's actually only one guaranteed point that we know is both on that line in the function. And that's the point of tendency. So we're gonna take this this X equals one, and we're gonna find out what the Y value that corresponds to this point is so I'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're gonna actually graft this on decimus. It's one of my favorite graphing utilities because it's free and online. Okay, so we'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'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't come, okay?


Similar Solved Questions

4 answers
9.2 (20 Pointh: Find the solution of the recurrence relation satisfying given initial conditions_ an-2 + Jn-] 6an = 0, n 20 initial conditions a = 0 ; 3, =5. b) an-2 8an-- 9an = 0, n 2 0 initial conditions a0 = 0 ; 3, = 10.
9.2 (20 Pointh: Find the solution of the recurrence relation satisfying given initial conditions_ an-2 + Jn-] 6an = 0, n 20 initial conditions a = 0 ; 3, =5. b) an-2 8an-- 9an = 0, n 2 0 initial conditions a0 = 0 ; 3, = 10....
1 answers
An archer shoots an arrow from a height of $1.14 \mathrm{~m}$ above ground with an initial speed of $47.5 \mathrm{~m} / \mathrm{s}$ and a launch angle of $35.2^{\circ}$ above the horizontal. At what time after the release of the arrow from the bow will the arrow be flying exactly horizontally?
An archer shoots an arrow from a height of $1.14 \mathrm{~m}$ above ground with an initial speed of $47.5 \mathrm{~m} / \mathrm{s}$ and a launch angle of $35.2^{\circ}$ above the horizontal. At what time after the release of the arrow from the bow will the arrow be flying exactly horizontally?...
5 answers
The ABC Boot Company runs two assembly lines In its plant The production manager wants t0 improve the Iine havinga monthly average of 11,350 units with & standard deviation of 050 the greater production variability: Line produces Line #2 produces 9,935 units por month on average with standard doviation of 996 units Which Iino will the units: production manager Improve? (must prove stalislically) (2 pls )
The ABC Boot Company runs two assembly lines In its plant The production manager wants t0 improve the Iine havinga monthly average of 11,350 units with & standard deviation of 050 the greater production variability: Line produces Line #2 produces 9,935 units por month on average with standard ...
1 answers
Second-Order DE, Roots of Auxiliary Equation Not Real $$y^{\prime \prime}+2 y^{\prime}+2 y=0$$
Second-Order DE, Roots of Auxiliary Equation Not Real $$y^{\prime \prime}+2 y^{\prime}+2 y=0$$...
5 answers
How many hour s ciapse bolkoon Ine Iirno commald sont Iromn Farth and the timo (no command receivod by Voyaner wiien (lared iterstelar : space? Exprase your anbwer Using two significant (guresAzd
How many hour s ciapse bolkoon Ine Iirno commald sont Iromn Farth and the timo (no command receivod by Voyaner wiien (lared iterstelar : space? Exprase your anbwer Using two significant (gures Azd...
5 answers
Magnified at 1000X. Estimate the size of each cell inmicrometers. Show your work for full credit.
magnified at 1000X. Estimate the size of each cell in micrometers. Show your work for full credit....
4 answers
This question is about quality management system.You are involved in establishing a start-up company that haslicensed a new chemical entity (NCE) with potential as a treatmentfor osteoarthritic pain. You are assigned to the team responsiblefor development of this product and are required to take it throughpre-clinical and clinical development.Before moving to Phase III, what requirements need to besatisfied, including the requirements from Phase II?
This question is about quality management system. You are involved in establishing a start-up company that has licensed a new chemical entity (NCE) with potential as a treatment for osteoarthritic pain. You are assigned to the team responsible for development of this product and are required to take...
2 answers
Let R be a region bounded by the four planes x=0, y=0, z=0 and x+y+z=9. Evaluate ∫∫∫24xdV over R.
Let R be a region bounded by the four planes x=0, y=0, z=0 and x+y+z=9. Evaluate ∫∫∫24xdV over R....
5 answers
What transformations are done to the graph of the function 𝑓(𝑥)= log3(x) to get the graph of the function g(𝑥) = −log3 (𝑥 + 4)? In addition, give an equation for theasymptote of the graph of g.
What transformations are done to the graph of the function 𝑓(𝑥) = log3(x) to get the graph of the function g(𝑥) = − log3 (𝑥 + 4)? In addition, give an equation for the asymptote of the graph of g....
5 answers
Find the derivative of the function log5 (1Oz5 ~ 3)50.4_3 1025 3af' (.)(50.4_3) In(5) f' (2) = (10z5_ 3x)50.4_3 (10z5 _ 3.) 1n(5)f' (2)f' (&) 10x5 _3xnone of thesef' (a) (10z5_ 31) In(5)
Find the derivative of the function log5 (1Oz5 ~ 3) 50.4_3 1025 3a f' (.) (50.4_3) In(5) f' (2) = (10z5_ 3x) 50.4_3 (10z5 _ 3.) 1n(5) f' (2) f' (&) 10x5 _3x none of these f' (a) (10z5_ 31) In(5)...
5 answers
Findff: (2x + Sy)dA where R is theparallelogram with vertices (0,0), (4,-5), (3,-1), and (7,-6).Use the transformation 1 = 4u + 30, y = 5u ~ UPreview
Find ff: (2x + Sy)dA where R is the parallelogram with vertices (0,0), (4,-5), (3,-1), and (7,-6). Use the transformation 1 = 4u + 30, y = 5u ~ U Preview...
5 answers
What is the volume (in cm of a 43.6 g piece of metal with a density of 2.71 g/cm3?none of the above19.50.42516.16.65
What is the volume (in cm of a 43.6 g piece of metal with a density of 2.71 g/cm3? none of the above 19.5 0.425 16.1 6.65...
5 answers
Lf e Ax = 26 then x =
lf e Ax = 26 then x =...

-- 0.023478--