Errors and root finding

Solve $f(x) = x^3 - x - 1 = 0$ (root $x^*\approx1.3247$). (a) Do two Newton steps from $x_0 = 1.5$. (b) Show $g(x) = (x + 1)^{1/3}$ gives a convergent fixed-point iteration on $[1, 2]$. (c) Compare the convergence rates.