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) $.
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