Question

A numerical solution of the equation can be obtained using Newton- Raphson method

$f\left(x\right)=2\sqrt{x}+3x-6=0$

If the starting value is $x$ = 3 for the first iteration, the value of $x$ that is to be used in the next step is

• A. 0.298
• B. 2.385
• C. 1.192
• D. 0.596

Answer 1

The correct option is C 1.192

$x_{n+1}=x_n-\frac{f\left(x_n\right)}{f^{\prime }\left(x_n\right)}$

$x=3,f\left(x_0\right)=2\sqrt{3}+9-6=3+2\sqrt{3}$

$f^{\prime }\left(x\right)=3+\frac{2}{2\sqrt{x}}=3+\frac{1}{\sqrt{x}}$

$f^{\prime }\left(x_0\right)=3+\frac{1}{\sqrt{3}}$

Then,
$x_1=x_0-\frac{f\left(x_0\right)}{f^{\prime }\left(x_0\right)}=3-\frac{3+2\sqrt{3}}{3+\frac{1}{\sqrt{3}}}=1.192$