In Newton-Raphson method, starting with initial approximation x_0, the next iteration is:

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SSC Applied Mathematics QUESTION #1308

Question 1

In Newton-Raphson method, starting with initial approximation \(x_0\), the next iteration is:

\(x_1 = x_0 - \dfrac{f(x_0)}{f'(x_0)}\)✔️
\(x_1 = x_0 + \dfrac{f(x_0)}{f'(x_0)}\)
\(x_1 = x_0\cdot\dfrac{f'(x_0)}{f(x_0)}\)
\(x_1 = -\dfrac{f(x_0)}{f'(x_0)}\)

Correct Answer Explanation

Newton-Raphson iteration formula: \(x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}\). It is derived from the tangent line approximation at \(x_n\) and converges quadratically near a simple root.

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