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The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$  is the derivative of $f$. The method converges

  1. always
  2. only if $f$ is a polynomial
  3. only if $f(x_o) <0$
  4. none of the above
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Answer: D

The method will usually converge, provided this initial guess is close enough to the unknown zero, and that f$'$(x0) != 0.

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