Question

Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 3 = 0. (Round your answer to four decimal places.) x2 =?

Answer 1

Answer:

$x_{2} = 0.0000$

Step-by-step explanation:

The formula for the Newton's method is:

$x_{i+1} = x_{i} + \frac{f(x_{i})}{f'(x_{i})}$

Where $f' (x_{i})$ is the first derivative of the function evaluated in $x_{i}$.

$x_{i+1} = x_{i} + \frac{x_{i}^{4}-x_{i}-3}{4\cdot x_{i}^{3}-1}$

Lastly, the value of $x_{2}$ is determined by replacing $x_{1}$ with its numerical value:

$x_{2} = x_{1} + \frac{x_{1}^{4}-x_{1}-3}{4\cdot x_{1}^{3}-1}$

$x_{2} = 1.0000 + \frac{1.0000^{4}-1.0000-3}{4\cdot (1.0000)^{3}-1}$

$x_{2} = 0.0000$