Multiple choice

The following equation needs to be numerically solved using the Newton-Raphson method. x3 + 4x - 9 = 0 The iterative equation for this purpose is (k indicates the iteration level)

  1. $x_{k+1} = \frac{2x^3 + 9}{3x_k^2 + 4}$
  2. $x_{k+1} = \frac{3x^2 + 4}{2x_k^2 + 9}$
  3. $X_{k+1} = X_k - 3X_k^2+4$
  4. $x_{k+1} = \frac{4x^2_k + 3}{9x_k^2 + 2}$
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A Correct answer
Explanation

Newton-Raphson formula is x(k+1) = x(k) - f(x)/f'(x). For f(x) = x^3 + 4x - 9, f'(x) = 3x^2 + 4. So x(k+1) = x(k) - (x^3+4x-9)/(3x^2+4) = (x(k)*(3x^2+4) - (x^3+4x-9)) / (3x^2+4) = (3x^3+4x-x^3-4x+9) / (3x^2+4) = (2x^3+9)/(3x^2+4).

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