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Problem 26 Medium Difficulty

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

$ \cos (x^2 - x) = x^4 $

Answer

$x=1,-0.73485910$

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Video Transcript

question 26. We are giving the luncheon co sign X squared minus X equals X to the Ford. So I'm gonna bring it all to one side sign Next. Weird minus minus. X to the four equals zero. I'm gonna take the derivative my nine equals Negative sign, Chain role X where minus X That's meeting times derivative of my inside Who? X minus one. And then I'm gonna take the drew tickle next to the fore, kids or thanks you now hiding things up just a little bit. I, uh Negative. Ricks Minus one sign X weird minus x minus. For home use. Newton's actually end plus one. He goes x to the n minus f of X over a crime s So that's when you get me extra n minus my function in green minus co sign X squared minus X minus X to the fore and my derivative, it should be read, and that's a negative. Do X minus one sign X squared minus x minus or excuse. All of that was in my graphing calculator. Give me a two routes. Have a room at one and an approximate room at 10.7. So I'm gonna start with Exit one is approximately negative. 10.7. When I put that in to my ass when X equals negative 0.7, my rules Negative points. Seven, three Hey, bye. A war 354 What I put that in for my ex My y equals approximately negative 0.73 Or be six, 274 And when I put that in my ex and ask why my fourth generation is negative. 0.7 34 eight by 910 which is also by exit pied. So I have equals one and my fourth and considerations of negative 0.7348510