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)

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Numerical Methods

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)

A) $${{\text{x}}_{{\text{k}} + 1}} = \frac{{2{\text{x}}_{\text{k}}^3 + 9}}{{3{\text{x}}_{\text{k}}^2 + 4}}$$ B) $${{\text{x}}_{{\text{k}} + 1}} = \frac{{3{\text{x}}_{\text{k}}^2 + 4}}{{2{\text{x}}_{\text{k}}^2 + 9}}$$ C) $${{\text{x}}_{{\text{k}} + 1}} = {{\text{x}}_{\text{k}}} - 3{\text{x}}_{\text{k}}^2 + 4$$ D) $${{\text{x}}_{{\text{k}} + 1}} = \frac{{4{\text{x}}_{\text{k}}^2 + 3}}{{9{\text{x}}_{\text{k}}^2 + 2}}$$

Answer & Solution

Correct Answer: Option A

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