Question

The equation $x^3-x^2+4x-4=0$ is to be solved using the Newton-Raphson method. If x = 2 is taken as the initial approximation of the solution, then as the next approximation using this method will be

• A. $\frac{2}{3}$
• B. $\frac{4}{3}$
• C. 1
• D. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{4}{3}$

$f\left(x\right)=x^3-x^2+4x-4$
$f^{\prime }\left(x\right)=3x^2-2x+4$
At $x_0=2,f\left(x_0\right)=f\left(2\right)=8$ & $f^{\prime }\left(x_0\right)=12$
Newton Raphson iteration:
$x_1=x_0-\frac{f\left(x_0\right)}{f^{\prime }\left(x_0\right)}=2-\frac{8}{12}=\frac{4}{3}$