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Consider the curveyl + %ly - 9y = -5 . Find the follawing: Find the slope of the curve at the point (1,1) (Hint: That is, find Zat (1,1)) [10&is]A tangent line ...

Question

Consider the curveyl + %ly - 9y = -5 . Find the follawing: Find the slope of the curve at the point (1,1) (Hint: That is, find Zat (1,1)) [10&is]A tangent line Irom the origin touches the curve at what %-coordinate? [5ees]

Consider the curveyl + %ly - 9y = -5 . Find the follawing: Find the slope of the curve at the point (1,1) (Hint: That is, find Zat (1,1)) [10&is] A tangent line Irom the origin touches the curve at what %-coordinate? [5ees]



Answers

Find the point on the curve $y=x^{3}-11 x+5$ at which the tangent is $y=x-11$.

Oh we want to find the slope of the tangent line at the point. 12 on the equation X cubed plus five X squared, Y plus two, Y squared equals four Y plus 11. For equation X and Y. Such as this, we have to use the process of implicit differentiation to identify dy dx the rate of change of the equation or function to do so. We followed the two steps listed here to solve for dy dx and then plugging dy dx at that point to obtain our desired slope first differentiating and return with respect to X gives the following, applying the derivative on the left side and right side gives us three X square plus 10, X Y plus five X squared plus dy dx. These two terms are for the product rule on five X squared Y plus four Y. Dy dx and the right side becomes four dy dx plus zero. We want to solve for dy dx. Let's isolate our dy dx terms as we do here, dividing by the polynomial most by dy dx that to solve our slope or rather are slow to point. Do I d x equals negative three X squared plus 10 X Y. Or five X squared plus four, one minutes. Four. Plugging in our 40.12 We obtain negative three plus 20/5 plus eight minus four. Or slow negative 23/9.

Today we're going to be finding the equation of the line that is tangent to the curve squared of X at the 0.11 I have provided the equation for the slope of this line, which is the limit as X approaches a of f of X men s f all abide by X minus A. In this case, one will be a We'll go ahead and plug in, uh, for this equation the limit as X approaches one of the squared of X minus the square root of one divided by X minus one. This is equivalent to the limit as X approaches one squared of X minus one over X minus one. Now we're going to factor the bottom the denominator of this X minus one. So this will say is the limit as X purchase one in the top will stay as X minus one. Over the bottom will factor in the square root of X plus one times the square root of X minus one. This is similar to, uh, X squared minus one. Re factored into X plus one and X minus one. Sorry, uh, X minus one But in this case are x squared is just X and R X is the root x so we can cross out screwed of X minus one and the limit as X approaches one now equals one over the square root of X plus one. And we can plug in X in for this equation. Now we have one over a period of one plus one. And of course, that's just too so that equals one half. Now, the equation of a line is why minus y zero equals M times X minus X zero and our X zero. Why is here, uh, equals 11 as given in the problem, and R M is one half as we just found so plugging in Yeah, Y minus one. It was one half times x minus one. And to simplify why equals on Half X plus one half, which is our final answer? Well,

Now this question wants us to find the equation of the tangent line of this curve at the point X equals two. So first let's find what why value This equation has X. Goes to And that's two to the third, which is 8 -7, which is 11 to the fifth. So it's one. So this point is to one. Now let's find the derivative which is a slope of the tangent line to the power rule. Now we need to take the derivative of the inside, which is three X squared. And that gives us 15 X squared times X cubed minus seven to the fourth. And we want to find the derivative When x equals two. So that's 15 times four times two to the third, eight minus 711 to the fourth. So 15 times four which is 60. So our line is going to have a slope of 60, so y equals 60 x plus some value B. And we want to know what this intercept is. So we know that at X equals two. Why is one? So let's plug in one and two to find this be, so B is one minus 1 20 which is negative 1 19 to our final line is why ICO 60 x minus 1 19.

To solve this problem. Do we have to understand the Chris Humble? Definitely. Why's you Amy? It's minus X one Ria Why you want either way on the line? We're image. Get me a slope of the tenant land. Do you obey the eggs? Sure. Here is even increase. It has to be Have to compute the Did you beat Debo? Why be suspect X So Take the liberty off the demon even in prison with this victim X So you can ID anyway The ex power up e It's a sweat less biased way. And you a dx Xing about of e highway My nose the way he is en route. Why is where a lot of these I've explained to you? Okay, we have to apply here. The general, because is a different constant X and light. Yes, So you have to apply the Hair channel And for Dr also here we have to have like the border so we can see as you know very well about Eka Power X derivative The power of ex schoolgirl. So we can debate about this sponsor is you seek The power of e is extra square plus by it's wet include the way D X in tow. Excess wear less. Why you swear? Now we cannot let the poor doctor you can get X in tow Day, Betty Bob Peak. A part of Ivy's UKIP are piped into do you a bay? Yes, plus weekend. I'm very eager about Of e is high buy into very, very about x is well, so much play with what began Also play here the productive soup Can I buy a square included Deliberate about this one I have X mate do in court today Go bless about of each have explained two different anyway T Bo, why is going to do it? You do anyway peaks Now we get simply by this one the power of eat extra square less why you sweat income Very pretty. But why you extra square each to x and the derivative. But why its qualities? No way to do it now weekend really high this dumb It's gonna go x in tow about of each easy boy. What into you anyway? Yes, Other privilege Plus a bout of each nightly Now bless I wise Well, but do I lies Webber group and I i why describe it to do You get power, I x right. I expect other damage plus Oh, because do I the power of each I expect a group in a drawer You do away DXE So can I. You know. Do you know that? Given what Really What did you do? Come on, let me feel the value of X is true and a little quiet What? So you can hear one who and what So you can play duel that true? It's quite a blessing Squared off goingto scrupulous due into one into do away dx Do it about up each hiring one into the way way ifs bolos part of e I've been to one but less I've been to one the power of these I'm goingto go in tow Cool crew in tow one into the power of these iron rule If I read too interview a bay bx No you can't sleep far Took apart tetanus four plus one about up each Hi, we'll take it Plus for 24 plus cool less cool. Do you ever? Yes. To be by here going through the part of each pipe into dualities We'll go power of high. Do you wait Wait BX Now we can get of each plus about of each. I bless I bet you in tow the power of speech. I beg you in tow And they got into the part of each Indra a plus. Bless Do in tow the power of these five in tow You away DX You see this? No, no, we can simplify. Pour into the power of please plus crew in tow. The bar is driving to delay bx crew in tow about of each pipe into view away. Yes, we can add this stuff so you can get seven by two out of each page that's going to you. Give our high Do you like Bay D's now again? This is a symptom Should begin. Cancel out Well said then you can get holy week about pipe minus seven. Doing Eka power by growing power. I can't be late peaks now Here you can get one day do into our high physical wounds. I've been to be way, Way x so you can get here can divide both sides by twin tweet apart pipe. Then you can get do you obey He X is equal to one day. I don't know if you ever DX is give the solo for that given so we can die image Monday. I don't know the gristle of the junior line age. Why is your aim in X minus? Excellent. Bless you. Really? It's why you want to quit. Who did what? All these Philip Disagree, sir. So we can get a bicycle to 14 X minus two. Bless one. Can I tear? Expect before minus one grade school. Unless what I know the answer is logically explain for less Glen Bay. Cool. Thank you.


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