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Numerade Educator

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Problem 9 Medium Difficulty

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) $.

Answer

$$
x_{2}=-1.25
$$

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Video Transcript

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