Consider the Newton$-$Raphson $($NR$)$ algorithm applied to the function $f(x)$ plotted below. Answer the

questions below based on the portion of the function shown in the plot

a$)$ Give an approximate range of starting $x$ values that should enable the NR algorithm to converge

to the second root $)$ of the function. Give as broad a range as you can while still ensuring

convergence and justify your choice.

b$)$ By means of sketches and a brief sentence or two, explain what would likely happen if the

starting value of $x$ was chosen to be $1\mathrm{.}0.$ Be as specific as you can; for example, sketch on the

graph above the sequence of $x_i$ values that would result from a NR algorithm starting at $x_0=1\mathrm{.}0$