Calculating Newton's Method: Step-by-Step Guide

[jisbon]

Homework Statement

Let $$f(x) =
\begin{cases} \dfrac{x^3-1}{\sqrt{x}-1}, & x > 1\\
cos(x-1)-x^2, & x \leq 1\end{cases}$$

Use Newton's method with $x_{0} =1$, compute the second iterate to approximate value $c$ where $c$ is a stationary value that lies in the x-axis for some $0<c<1$

Relevant Equations

-

Since the Newton's method is as follows:

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

$$x_{1}=x_{0}-\frac{cos(0)-1}{-sin(0)-2}$$

Is this correct? What should I proceed on from here?

 

[Mark44]

Homework Statement: Let $$f(x) =
\begin{cases} \dfrac{x^3-1}{\sqrt{x}-1}, & x > 1\\
cos(x-1)-x^2, & x \leq 1\end{cases}$$

Use Newton's method with $x_{0} =1$, compute the second iterate to approximate value $c$ where $c$ is a stationary value that lies in the x-axis for some $0<c<1$
Homework Equations: -

Since the Newton's method is as follows:

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

$$x_{1}=x_{0}-\frac{cos(0)-1}{-sin(0)-2}$$

Is this correct?

Yes, as far as you went

What should I proceed on from here?

Evaluate cos(0) and sin(0) and substitute in the value for $x_0$.