Chapter 4.7, Problem 40ES

(a) Use a graphing utility to generate the graph of $f\left(x\right)=\frac{x}{x^2+1}$ and use it to explain what happens if you apply Newton’s Method with a starting value of $x_1=2$ . Check your conclusion by computing $x_2,x_3,x_4,$ and $x_5$ .

(b) Use the graph generated in part (a) to explain what happens if you apply Newton’s Method with a starting value of $x_1=0.5$ . Check your conclusion by computing $x_2,x_3,x_4,$ and $x_5$ .