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Question

10. [-/1 Polnts]DETAILSMY NOTESASK YOUR TEAFind (If possibic} the rattonal zeros 34X2function {Enteryou ans ercomma-separteonanser does not exist, entcr DNE.)Need Help?Aocm(-/1 Polnts]DETAILSMY NOTESASK YouR TEACDouilble Lhe rlona {#to"the functon Mmur Gocomma-separated Ist. Mun nGei does Doraln Mmer DNE.)77 79 2Need Help?

10. [-/1 Polnts] DETAILS MY NOTES ASK YOUR TEA Find (If possibic} the rattonal zeros 34X2 function {Enteryou ans er comma-separteo nanser does not exist, entcr DNE.) Need Help? Aocm (-/1 Polnts] DETAILS MY NOTES ASK YouR TEAC Douilble Lhe rlona {#to" the functon Mmur Go comma-separated Ist. Mun nGei does Doraln Mmer DNE.) 77 79 2 Need Help?



Answers

$7-10$ Verify the given linear approximation at $a=0 .$ Then determine the values of $x$ for which the linear approximation is accurate to within $0.1 .$
$1 /(1+2 x)^{4} \approx 1-8 x$

This problem were given the table of values which are in the upper right corner and for part. And you want to know what is the equation? That accident, symmetry of their problem. So the way we find this is we look at the table and find where they're symmetry around. What value. And as you can see, you have 93139 So we have axis of symmetry around this one value and same thing for X. We have negative 21012 So our access and symmetry is around this point and spur the equation. Since it's a problem, we know that it's gonna be a vertical line. So our equation for axis of symmetry is going to be X equals zero. Then for part B, we want to find the minimum or maximum value of the function and the value at of Z. I want it occurs. So as you can see, we around our axis of symmetry on both sides, the values of FX increase on both sides. So that means our proble is opening up words. So we're gonna have a minimum value value and that minimum value is gonna occur um, at that same 0.1 So we have a minimum, uh, one at X equals zero, Then for part C, we want a sketch, a graph of the function from the values given in the table. So we're just going to grab it. So what? Negative two were at nine. Negative one. We're at three. Zero were at one on at one. We're at three and that you were at nine again. So are probably looks something like this. And finally, for part D does dysfunction have riel or nuns? Rials. Zeros. So, looking at our graph, we can see that our function never crosses the X axis. And that's what would indicate a really zero if it crossed se X equals negative two or two. But since paragraph never crosses the X axis, we know that paragraph has no one really zeros

In this question, I'm going to use on, like, Catherine calculator and it's called the Decimus. Yeah, the function were given is F X go thio minus thio expound three minus six X power to last three. So when we look at the graph of the function here, we see that between the interval from minus three to minus two. We see we have one solution there and we can confirm that using the intermediate value theory, um, so and the value of minus three, we will have the value of the function ico thio we see here and we'll go with you. Uh, it would be positive there on day, then after that, we see on the value minus two, we see the value of the function is negative. Therefore, we have one solution between the interval from minus three to minus two and exactly the solution here coaching minus 2.81. Similarly, between the interval from one minus 1 to 0 we see and the minus one value on the function is negative on and zero, the value of the function is positive. Therefore, the value of the function changing from negative to positive and then we have one solution in that interval. And exactly the Social Hecho Jenna minus 0.832 and the last zero here will be between the interval from 0 to 1. So and so we have the value of the function responsible and and the one we have the value of the function here it go to the negative and therefore we have one social between the interval from 0 to 1 and exactly the only echo to the 0.642

This question I'm going to use online Catherine Calculator in his corner this month. He had a function were given is our ex Oh Thio, Expel Far minus can express Jew plus two. So look at the graph. Here we see we have the late four zeros here the first zero here we see in the girls in the interval from minus 40 to minus one we see down from minus four to minus from minus 40 minus three and the value of the function changing from constitute thio negative here. Therefore, we have exactly one assertion in the interval from minus 40 minus three and exactly the zero here equal to minus 3.13 Similarly, for the interval from minus 1 to 0 the value of the function changing from negative to the positive here and therefore we have another zero here and exactly the value in equal to the minister 00.452 And now for the next zero in the interval from 0 to 1, the value of the function changing from constitution negative and we have another zero here equal to deserve on 45 to the last zero occurs in the interval from 3 to 4 from three to find the value of the function changing from negative to the positive one here. And if I would have one throw there and exactly the equal to the 3.13

For the given problem, we're going to what find after Becks, which in this case is we're gonna graph it so we have the F of X. Is equal to execute minus X squared minus two X. Okay, last one. And this gives me over the interval from 0 to 1. So we're going to look at F of zero and everyone, you know, continuous over this interval and we go from a positive number two, a negative number. That must mean that there's a zero in between there somewhere. So if we look at 0.5, for example, That's negative, 0.4 is positive and 0.5 is negative So we can squeeze in closer making this your .45, Making this 0.42 43 For We said that once we get 45, that's when it goes negative. So it seems to me between 0.44 and 0.45 And we end up getting our final answer to be 0.445 and that's the final result.


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