5

Point) #fl) = 6 + 6x Sx? , (ind the equation of the line tangent t0 the curve f(x) atx = -4.The tangent Iine Is y...

Question

Point) #fl) = 6 + 6x Sx? , (ind the equation of the line tangent t0 the curve f(x) atx = -4.The tangent Iine Is y

point) #fl) = 6 + 6x Sx? , (ind the equation of the line tangent t0 the curve f(x) atx = -4. The tangent Iine Is y



Answers

Find an equation of the line tangent to the following curves at the given point. $$x^{2}=-6 y ;(-6,-6)$$

This same. They'd like us to find an equation to attention line. So it's fine. Darter. So we'll have. Let's see and put one over in. So that's negative. Six over the in but squared, then times the derivative of. But that's just two X. So to get slope, we can plug in that negative and we'd end up with Let's see the negatives will cancel UPS would be positive. At the top It be 24 over. Let's see negative two on the bottom and four plus four. Hey, where it is, This is what we get. Let's see, we have eight squared on the bottom and eight times three on top. So we end up with three over. It has our slipped on. Let's see what point. Negative two and put corresponds over. Hey, the over. So the point negative to 3/4. Let's find the equation of the tangent plane that passes through that point. Hope minus 3/4. See our slope every on the next. So we have one is equal to three over A. We have a plus three over foreign, plus 3/4 that's actually plus 6/4. I mean, are 3/2. In other words,

Function at six over X Squared plus four, and they want us to find the tangent plane at a is equal to negative T. Well, let's find that y value will unemployed. Let's see. 6/8. Well, that's three over foreign. Okay, Does that seem very yes, I have. Let's find a slope so we'll take our derivative well in the West. Let's see six. Yes, we have won over the input to the negative to power. Oh, and the most played by negative one in front and then times the river of the inside much is two x so on the voice. Let's see. Negative Seo on the moon. Just square tomorrow where now we have negative 12 x over X squared, plus four squared. So what happens when a plug in negative to what we end up with? 24 over? Let's see, we have eight squared, so over is 64. Well, we can divide the top and bottom before actually going to write about eight. So end up with three over. Let's see a That's a slope so we can use their point. Slow formula will have three over for equal. Let's see the slope 3/8 minus X plus team. And now let's see our equation for it. Angelyne is wise equal to three over a X Let's see, plus 6/8, plus another 6/8. So that's a plus 12 over Blessing Marine. Let's see. Yeah, looks awesome.

In the given question were able to find a situation of pendant for the graph The graph is I can say that vax it was too -1 by to execute -1 by to execute. And it is said that the attendance should be parallel to the line. The line is given us notice six x plus y Plus 42 West Regional. Okay, our tendons should be parallel to this line. So first of all I am writing here slope of this line Slope It was two -A divided by B means minus six, divide by one means minus six escape. Now if I do friendship this card then I get -1 by to multiply 30 x is squared. OK. And you know that this derivative represents slope of the tangent. Okay, this represents slope of pendant and it is said that in the question yeah tangent is better than to the dividing line tendencies that a little to give a night. Do they need them slope of this game online should be. It was to global tendered. Okay. Do do do anything Slowpoke tangent is requesting slope of given a light so slope of tension that is -1. Going to into three. Access would Equals 2 -6. From here. You're minus against loads and you finally get three access where it was too Well after that we get access where it was too food. Okay? And after that we should get tax, it was too plus minus took. Okay? No, we have to flounder well, Wolf right here, it's a good here. You can see that if we could well well X that is to And we should get -1. Vital to kill That is it was true -4 And if I put -2 then I get minus one by two, divide by minus two cubic was 24 And finally I can say that if access to the point that If access to then write -4 and if X is minus student, why is for and that's slow. I can say that Tax was too then why is -2 for -2 days. For? And the slope is -6. Okay. Died. Uh, I am writing the activation of attendant activation of attendant. Okay. For first of all the point that is to form I -4. By the formula that is y minus Y. When it was to maximize minus X. Y. And tom your wife plus four equals two -6 X -2. Why? Bless fort it was to minus six X plus two world and told me we should get six X plus Y. It was to it And it's a very articulation of 10 years for the next point. Immigration opinion for the other point, Another point is -2 or more four, and I should get why minus, for it was true 2 -6 x plus two. But I'm here by minus 40 Western minus six X minus 12 six x plus y equals 2 -8. Okay, So these are my both equation of vengeance, since there are two points given. Okay, Thank you.

Mhm Problem # 49 is an equation of a tangent line problem. That requires us to find the equation of the tender line to this given function parallel to the line given. So we'll start by differentiating the function using the power rule. So we'll get negative three halves X squared. And then we'll need to, since it's parallel of this line, we want to find um what the slope of this line is because we know parallel lines have the same slope so I can rearrange this into slope intercept form To find that I need a slope of -6. So we can also use derivatives to find the slope. So try something derivative equal to that slope value. I'll find what X value would produce that slope. So I can do negative three halves, X squared equals negative six. And I can multiply both sides by -2/3 to clear. The fraction I have X squared equals 12 divided by three is 4. So x equals plus or -2. So now I can choose one of these points to plug into my original function to find the Y value at that point. To complete the point of tendency that I can use with the given slope to write the vision of the life. So if I do F of kill and I have negative one times to cuba It's very negative 1/2. So negative 1/2 of eight is -4. So I have a slope of -6. and the point 2 -4. That I can use with point slope form my minus wise of one equals M times X minus except one, which I can rearrange into slope intercept form if I'd like That -6 x last as one answer. And alternatively, you couldn't have completed this process finding F of negative two as well. But since you just asked for an equation, not all the equations this one will do.


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