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Problem 32 Medium Difficulty

For the following exercises, given the function $y=f(x)$
a. find the slope of the secant line $P Q$ for each point $Q(x, f(x))$ with $x$ value given in the table.
b. Use the answers from a. to estimate the value of the slope of the tangent line at $P .$
c. Use the answer from b. to find the equation of the tangent line to $f$ at point $P .$
$$
[\mathrm{T}] f(x)=\frac{x+1}{x^{2}-1}, P(0,-1)
$$

Answer

a. See table $\quad$ b. $m_{P Q}=-1 \quad$ e. $y=-x-1$

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IK

Ibrahim K.

September 24, 2021

speak louder please

IK

Ibrahim K.

September 24, 2021

IK

Ibrahim K.

September 24, 2021

IK

Ibrahim K.

September 24, 2021

Video Transcript

forget it. We have f of x x post one over excluded much one and p of zero negative one were asked to find the bowling's table, so we have Thanks. And this little peek you x and this slope them pick you off the values zero points, one show points still 1.1 No point sounds owns no one. Is there a point sales? So the one in and one more. 12345 And then we're asked, if I'm a shame for the negative values. Um, well, that is it. 12345 Okay, well, let's start with Exit Eagle one 0.1. Q is equal to 0.1 and f evaluated. Appoint one. Use me. I'm the 1.11 and in our m p. Q. That's equal to negative 1.11 Linus, close one all over 0.1 minutes. Gives me 1.1 negative of it. Get negative 1.1. Okay, and then that's about weeks. That X is equal to point. Don't want what we get. Cute. Is there a 0.1 and f evaluated at 0.1? Is the negative 0.1 Negative. 1.1. Okay, Now finding our slope yet it is 1.1 like this, plus one over zero point. No one That gives me in the one point. It seems like our slope follows a pattern. When we have it's basically are accused. Why value always. Okay, well, yet negative points. One point. Okay. And it's look for X is equal to 0.1 Well, aren't you going to put it to one and f evaluated at 0.1 from Jill? Don't one. You're sweet native 1.1 M p. Q iniquitous negative. One point when plus one over a joke. Wait, Josie One. Give me what point does out negative of it. Okay, So if you notice we also have a pattern for arse look. Values cedars to girls. And in a 1 to 0 a minute, one and one cell in a one. So our next slope followed the same pattern so that negative one points. So? So? So you get a one point, it'll sell. Oh, no one. You want to fight? Why? I don't want to be 45 Okay. No looking for our negative. Vialli's looks Look at that exit equal to negative one. What I mean Q is equal to like you of the good of 0.1 and evaluated at a good point. One. Who's he seeing? Excuse me? Negative points 90 And then I assume, based on our previous values are slope will be the same as this rally. So we have Good. Is there a point tonight? So your next pattern for execution to negative 0.1 Q is equal to negative 0.1 and then putting in of negative zero point. You're one. Yes. Negative points. 99. Okay, so we do also have a pattern here. Notices a 119 here and one girl here. But over here we have two zeros are two nines and two girls. So if our pattern is Crabtree a 0.9 So you got to get herself a three and threes ills, and then you can follow this pattern. So poor nines and imports are old. And then five nines I'm Selves. 123452345 and six Things. 123456 and 60123456 Right. Okay, so we feel that our table so now for part being were asked to trigger out what the slope is. Well, it seems like as we get closer to the values of zero, we're approaching negative one. And if we get closer Yeah, so from this way and this way, are approaching a good one. So we can say our slope is negative one, and it's fine attendant lines. What? Why is it too? And what you get a one X bust feet? I'm plugging in one of the points we know. Well, uh, points one because he could What's one plus one over? 10.1 squared, minus one. So you get 0.1 plus one. Why don't Black white one squared minus one. You get negative 1.11 Can't stop looking. That n word yet? Negative 1.1 physical check. 0.1 negative. White one must be okay. Now it's attracting this. Yes, for adding point. One of the upsides. You're good. Negative. 1.1 is approximately equal to that one, which is equal to be so, uh, are changing. Mine is equal to y is equal to negative X minus one