Chapter 6, Problem 16P

(a) Apply the Newton-Raphson method to the function $f\left(x\right)=\text{ tanh}\left(x^2-9\right)$ to evaluate its known real root at $x=3$. Use an initial guess of $x_0=3.2$ and take a minimum of four iterations. (b) Did the method exhibit convergence onto its real root? Sketch the plot with the results for each iteration shown.