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Question 3 (70 Points) Use Muller's Method for the below function in the interval [0 , 2] and find the value of € and a for the following quadratie equa...

Question

Question 3 (70 Points) Use Muller's Method for the below function in the interval [0 , 2] and find the value of € and a for the following quadratie equation p(v) av + bv + €f(x) =x3 +3x2 _ 1

Question 3 (70 Points) Use Muller's Method for the below function in the interval [0 , 2] and find the value of € and a for the following quadratie equation p(v) av + bv + € f(x) =x3 +3x2 _ 1



Answers

In Problems 73 and 74 (a) Use the Intermediate Value Theorem to show that $f$ has a zero in the given interval. (b) Use technology to find the zero rounded to three decimal places. $$ f(x)=x^{3}-x+2 \text { in }(-2,0) $$

This is asking us to find the relative extreme of this function and also find inflection points. So what we do is we take the derivative said it equals zero to find critical points first and taking the derivative if he's practical. So this ends up being minus he to minus to you minus to honesty. Times eat a dynasty, okay? And then said this thing is equal to zero. Divide out by eating the modesty. You know, we have so anything about factoring out nine inviting, but this gives us minus one minus two. Rusty equals zero, sir. Tea. Oops. T is equal to three. Let me take our second derivative of G. You'll be finding inflection points. Anyways, I just use this as we use the second test. So it's just going to be e to the minus. T causes negative two negatives for this first term. Then we need to use a project with them and it's suspended. Close you to my honesty. Okay, then it's going to be plus, so be careful with your negative signs to minus t he to the modesty distributive either Modesty is minus one minus t right. So that gives us the snake plus sign through to this thing. That two minus t gives us this plus sign. So no, he said this thing, You was your own self. Someone get to plus two more. Honesty equals zero, sir. Tea. It's equal to four, Right? Let's just check where Cohn Cavity is, and then we'll be able to get our inflection points. And our relative extreme on won't go, so tickles for so when t equals, let's say, um zero here. What do we get? We get one plus one was, too, which is definitely positive. So our con cave up here and then we have when we're bigger than four. Let's say t equals five. He has These are all negatives, and you have a negative here. So you have an inflection point here, abbreviated as I p. This is our inflection point. And then well, since the second derivative. Okay, so combining these two things together, Sergi, is Kong cave down there? Can't give up that the critical point t v equals three, which means, uh, he has a local. Then at T equals three go. So if you want to calculate what the values of these minimums are you can calculate G three, which would give us one minus E to the minus three. You could also calculate G four, which gives us see if there's enough room one minus two. I mean to the minus before. So if you want the help of a lease rather those now you got him.

In this question, we are going to find the absolute maximum and minimum I have, which is X multiplied by you to sex or two on internal from 93 to 1. So first we take the relative of lab by using products through. We got prime is just and then we set it equal to zero to get a critical number. Mm. So after the calculation, we got executed. Two negative two is a critical number. And then when you two did her mind a Texaco connected to is why maximized or minimized. So in order to do that, we need to pick up two numbers. One is smaller than active, too, and one is greater than NATO too. So I picked zero and negative five or two. And, uh, after plugging them into have prime I got when x ico 20 have primal zero is greater than zero, which means I think it's increasing on the interval from 92 to 1. And when I asked you to equal to 95 5/2 primaries smaller than zero. So which means that I feel is decreasing on the interval from 93 to 92. So X equal to 92 is when, uh, FX is maximized. And then we need to check the edge points on the interval from 9 to 3 to one. So by plugging 93 1 into us, we got to values one is about 90 0.669 and one is square than zero. And then we pro connected to into us, and we got a no value is about 19.736 So this one is the smallest. So that's the minimum and the long borders and zero is a maximum. So we can conclude that the maximum is when Mexico too negative too. And as well is Uh huh, No. Also, the minimum wage is when X is equal to negative two and the absolute minimal minimum they will put up with this. And when I execute one, we got the absolute maximum while you have, which is this

Harry. So here our local men Local minima is right here in the point I marked a which one? You're why? Value of negative 5.8 Where X is negative 1.15 Your local maximum is here at point B where you're why that you would be 1.8 and your excel you would be 1.15 You're decreasing where it's blue and you're increasing where it's green

We have X Squared plus six act last five over X month. This three. So we know right away that being an X squared and X to the first so that we don't have, there's no horizontal. Ask them to and where we factor this we get X plus five X plus one over X minus three. So are vertical Assam toad would be every it's really at X equals X equals three and we know that we have X such that X cannot equal three.


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