Chapter 13, Problem 11P

Determine the minimum of the function from Prob. 13.10 with the following methods:

(a) Newton's method $\left(x_0=-1,{\epsilon }_s=1\%\right)$

(b) Newton's method, but using a finite difference approximation for the derivative estimates.

$f\text{'}\left(x\right)=\frac{f\left(x_i+\delta x_i\right)-f\left(x_i-\delta x_i\right)}{2\delta x_i}$

$f\text{'}\text{'}\left(x\right)=\frac{f\left(x_i+\delta x_i\right)-2f\left(x_i\right)-f\left(x_i-\delta x_i\right)}{{\left(\delta x_i\right)}^2}$

where $\delta =\text{a perturbation fraction}\left(=0.01\right)$. Use an initial guess of $x_0=-1$ and iterate to ${\epsilon }_s=1\%$.