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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 $(-1, 1)$.

## $$x_{2}=-1.25$$

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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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