Use Newton's method to approximate a root of the equation:

Question

4x^3+8x+1=0 as follows.

Let x1=-1 be the initial approximation.

The second approximation x2 is:  

and the third approximation x3 is:  

Answer 1

x_n+1 = x_n - f(x_n)/f'(x_n), n = 1, 2, 3, ...

f'(x) = 12x² + 8; x₁ = - 1; x₂ = - 0.45; x₃ = - 0.1657718

Answer 2

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