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Use Newton's method to find all the roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.$x^{6}-x^{5}-6 x^{4}-x^{2}+x+10=0$

$x=-1.93822883$$x=-1.21997996$$x=1.13929374$$x=2.98984102$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

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In mathematics, precalculu…

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In mathematics, a function…

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Use Newton's method t…

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03:24

03:38

01:56

07:27

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For the following exercise…

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Hello. Everybody won't want to solve the problem. Number 174 Nielsen method which is using to solve money in the equation and one of the draft application. Okay. At first we have to remember our steps to get the results. Okay. Step number one. We have to get the derivative f dash X. At step number two. We have to use initial solution or initial value for X. That will be given in the question or we have to as you. It's okay. And the third step is the instituting and newton formula X. N plus one equal Xn minus F of X earned over f dash of X. And Okay so it's a question we have uh thanks equal extra 46 -5 -6 X. to the power four minus X to support to Plus X. Lost 10 equals okay, so the function, the derivative of the main function it will be equal six x to the power 550 -24 extra parts for you -2. It's lost one. Yeah. Okay. Okay. So when we get the graph over that main function, it will be like that. So we can note that there are two, there are four intersected points between the main function and X axis. The first one at 2.4410 and 10 and negative 4.8 93 Was zero and the -2.469. Okay, so now we have to get that point by using notes and medals. Okay, so let's form our our tables by using any calculation cheats. You can use the associate for example. Okay, so the first one for the first one we can use one potential solution and give us Muslims the same value after two on two traditions. Okay, so the first one will be equal one. The first solution. Okay, for that second one we can assume 2.5 as initial solution. So it gives us For eight digits of the science. Okay, It almost the same value of the fourth access separation. So the first The 2nd 1 is 2.4 Or or 94 94 1. Okay. And by the same concept and the same steps for the third one we can use negative one as initial solution and as the nearest point uh or nearest value for the second point. So it gives us After 4th and first iteration almost equal the same value. Okay, so the second the third one is negative 4.8930679 to 5. Okay, so 1, 3456788 digits after signed. Okay, so you're that's right. Okay. For the last one You can use negative 2.5 at the initial solution. So it gives us after 30 third story three attrition at the 2nd and 3rd generation, it almost the same value. So the fourth one or the last one equal will be equal. Almost equal negative 2.468 99 44 3. Okay, so that's that's all the fall. The four solution for the main function. Okay. Or the four routes for the main function. Okay. Thanks for watching and this year littering the next methods Nielsen Method application.

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