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Use Newton's method with initial approximation $ x_1 = -1 $ to find $ x_2 $, the second approximation to the root of the equation $ x^3 + x + 3 = 0 $. Explain how the method works by first graphing the function and its tangent line at $ (-1, 1) $.

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$$x_{2}=-1.25$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Derivatives

Differentiation

Volume

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Use Newton's method w…

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The first thing we can do is we can find the derivative of the equation being given, which gives us three X squared plus one. Now we know, except to is Axl Juan minus F of X one over prime of X one, which gives us negative 1.25 now to Graff. As we can see, this gives us our next approximation and then drawing the Tangela excess negative 1.25 We know x two is negative. 1.25

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