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ECTED VIEW Home Insent with Type Find Be careful points) all followed by at the point (2 , the files Design H from ~The 3.85) equation of the 3 Layout Hi Intcmnet tangent References 173 3 1 line contain assignment decimal line Mailings the places U graph Unless vou Review the of the 17 (Protected goren 01 paau View equation edit View) equation Tell me Word at (2. (s8 =Print or neally sketch the graph of4and the tangent line 1

ECTED VIEW Home Insent with Type Find Be careful points) all followed by at the point (2 , the files Design H from ~The 3.85) equation of the 3 Layout Hi Intcmnet tangent References 173 3 1 line contain assignment decimal line Mailings the places U graph Unless vou Review the of the 17 (Protected goren 01 paau View equation edit View) equation Tell me Word at (2. (s8 = Print or neally sketch the graph of 4 and the tangent line 1



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Draw a graph from the following data. Draw tangents at $x=2,4,6$ and 8 . Find the slopes of these tangents. Verify that the curve drawn is $y=2 x^{2}$ and the slope of tangent is $\tan \theta=\frac{d y}{d x}=4 x$ $\begin{array}{ccccccccccc}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}$

Hello. We have to find any personal attention lying to the gravel at the given point minus four comma to roll three. So for funding the 10 year land first we retired to calculate the slow, so we know that the slope is divided the X and we will calculate hate by differentiating that given function so divisive. Ideas of the given function. Square by square minus nine X squared minus four by a square cost to zero so it will be equals two and we differentiate echoes Karkovice Square by the grand old, so it will be caused to two x y Square plus to access square by divide by DX minus 18 of X, minus 85 Divisive ideas Because 20 From here we can divide idea because to two x y squared minus of 18 x upon a two by minus two x squared by So the slope of the tangent M he calls to develop DX at the given point, minus four comma 23 will be close to to multiply by minus four. Invite to rule three square minus of 18 multiplied by one is four upon a multiple. I went to Rule three one is to when I was four is squared and multiply it by two room three so it will be equals. Two minus eight multiplied way 12 minus of my husband is a plus 18 to 4 upon 16 3 minus all 64. Rule three. So the slow mm will be close to minus of 96 plus 7 to 2 upon minus of 48. Room three. She will be close to minus of 24 upon minus of 48 Route three. So it will be close to mhm. Vanna Bonta. Go through three so we can write the equation of tannin at a given point. X one by one minus four Comma 23 will be by minus Violinists 23 He calls to slow am multiplied by X minus. Excellent. Further, we can solve it by manage twice or three calls to the slope is one upon to route three X plus four. So it will be close to ex upon to Route three plus go upon room three plus 23 and further We can solve it so it will be equal to y equals two x about to route three plus eight upon Lord T, it will be your answered. That's it. Thank you.

Mm. The topic of this question is product and quotient rules. And this question asks us to find uh the equation of the line tangent to the curve given by this equation at this point. So to find this equation of the tension line. First, we have to uh well, first, let's consider the equation we know since it's a line that it can be written in the form Y equals M times X plus B. Where M is the slope and be as the Y intercept. Okay, now, uh by our knowledge of handed lines we know. So say we have a curve and a tangent line to the curve. We know the tangent line after the point of tendency must have the same direction in a sense as the curve. So it must have the same slope at that point and slope of curves we describe as derivatives. So if this curve has equation H of X, it's derivative which will will be H. Prime of X. And depending on what this X value is, uh the slope that derivative or the pounds at that point, the derivative will depend on the value of X at that point. So if it were the slope at two, uh then that would be a prime of two. So since we want to find slope of the tangent line, we want to find the derivative of this and X equals negative two. So let's differentiate using the product rule. Since that's the topic of this question. We can write this square as a product so that we can use product rule, although it may be easier to use chain rule if you know how to use that. Yeah. Yeah. So we to do the product rule, we have the two terms which I will call F entity two expressions. So the derivative of age, which is F times G is the derivative of us times three. Yeah. Plus the derivative of G. Which is the same as if time's up, which is the same as geek. So we really have just double of this. And since we want to find a prime at negative two, we substitute in X equals negative two. And so our slope of the tangent at that point is negative 24. Mhm. Yeah. Oh we want to find the right intercept of this tangent line. We know it's slope is negative 24. And so it can be written like this but we need to find A. B. And so if you know the formula for tangent lines have a special form, then you should use that because it is easier. All you have to do is put X. Subtract the X coordinate of the point of tendency from X directly. And then that gets multiplied by the slope. And then to all of that all together you add the y coordinate of the point of tangent C. And so that is our tangent line. Right? And so we had minus 48 plus nine which is minus 39. Yeah, except there is our tangent line. Now if you don't know this formula yet, I would encourage you to get to be familiar with it because it really helps. But uh get comfortable with the idea or if you don't want to use it yet, then you can also substitute this point into this equation to find B. And you would also find the answer to be negative 39. Now we want to graph this and so that's simply done. That can be simply done. Using days most this online graphing software we have our curve x squared minus one squared and the line is minus 24 x minus 39 because the slope is minus 24 and the Y intercept as negative 39. And so there we go. The point of tangent c minus 29 is right here somewhere.

Hello. We have to find any question of their tenure. Land to the graph at the given point, one comma one For this first, we will calculate the slope of the tenant and to fool the slope of the tangent. First, we will differentiate of this equation with respect to X. So from here we will get to our D X and at the given point when come open, that'd irrigated by with the access called deuce block of that engine. So first steps differentiate of the situation with respect to X the upon the X vice square X square place What is square? Because he upon the eggs great of a prescription so we can solve it by the general. So the differences in or vice grace Dubai divide by DX multiplied X squared plus y squared yes, differences and OPEC's sculptures Very school will be to express to white divide by DX monthly played by very squared because to four x and further we can simplify it and we will get beaver Idea X equals two four x minus two xy squared upon to y yeah square plus why is squared plus two like you and the slope of the tenure and that 0.1 comma Wanna If you constantly evolve adx at one comma one bill the quest to four minutes to upon two multiplayer two plus two because to do upon 6 30 recalls to one by three so we can write the equation. Attendant equation of Daniel had point. Excellent comma violent. That is because to one comma one so it will. Because two y minus y when it comes to M. Slope, multiplied by experiments. Expand. So we will put the value of x one and violent and slope Hickman is one. So it will because to one by three x minus one by three plus one so it will be equals to one by three of X plus two y three. That's it. I hope I answered the question. Thank you. Mhm.

Hello. We have to find any question of the tenure Land to the graph at the given point. Four Comma two. First, we will calculate the slope of the tangent line by differentiating like given occasion with respect to X, so it will be close to three multiples way too X squared plus y squared and the differences in of this access couple advice Carbon Me two of Express to ABI Divide Way DX will be close to two x minus to buy a DVD B D. X. So from here we will simplify it and it will be equals. Two. Divide by DX calls to 50 X minus three X Like a square place why you square upon three x squared plus y squared multiplied by by plus 15 white. So the slope of the tangent and because divisive ideas and they're going to 0.4 comma two so it will be close to 15 Multi berry four minus three multiplied by four 16 plus four upon three 16 plus four multiplied way cool plus 15 multiple way, too. So the slow be because to minus two y 11 and we can I the equation of the tenant equation of stagnant at point four common tools. It will be close to y minus Why, when it comes to slope him, multiplied by x minus X one. So it will be, comes to my mind, is driven by one is two and slow page minus to a 0.11 and X minus explanation for for the solving it bicycles to minus two upon 11 thanks plus at 1 11 plus two, so it will be equals two minus two upon 11 x plus 30 a born 11 there's it.


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