Multiple choice

The equation x3 -x2 + 4x - 4 = 0 is to be solved using the Newton-Raphson method. If x = 2 is taken as the initial approximation of the solution, the next approximation using this method will be

  1. $\frac{2}{3}$
  2. $\frac{4}{3}$

  3. 1
  4. $\frac{3}{2}$
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B Correct answer
Explanation

$\text{We have} \\ f(x) = x^3 - x^2 + 4x -4 \\ f(x) = 3x^2 - 2x +4 \\ \text{Taking $x_0 - 2$ in Newton - Raphson method} \\ x_1 = x_0 - \frac{f(x_0)}{f(x_0)} = 2 - \frac{2^3 - 2^2 + 4(2) - 4}{3(2)^2 - 2(2) + 4} = \frac{4}{3}$

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