Problem $14$: Newton's Method $[2$ pts$]$

Use the graph below and the initial guess tilde$(x{)}_1=1$ to graphically find the estimated solutions tilde$(x{)}_2$ and tilde$(x{)}_3$ for $f(x)=0$ using Newton's Method. Clearly indicate your drawings on the graph to show how tilde$(x{)}_2$ and tilde$(x{)}_3$ are found. Will the solution sequence tilde$(x{)}_i,$ where $i=1,2,3,4,$cdots, converge to the zero at the origin? If not, what would be a better tilde$(x{)}_1$ if you want the Newton iterates to converge to the zero at the origin?