$\"\"$

The function $\"\"$ , where the initial guess is $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

Newtons approximation method formula : $\"\"$ .

$\"\"$

Consider the initial guess $\"\"$ .

Newtons Formula : $\"\"$

$\"\"$

By using newtons method the initial guess $\"\"$ is failed.

$\"\"$

Newtons approximation method is failed for initial guess $\"\"$ is failed.