Answer
$x_{3}=-0.6825$
Work Step by Step
$f(x)=2x^{3}-3x^{2}+2$
$f′(x)=6x^{2}-6x$
$x_{n+1}=x_{n}-\frac{2x^{3}_{n}-3x^{2}_{n}+2}{6x^{2}_{n}-6x_{n}}$
$x_{1}=-1$
$x_{2}=-1-\frac{2(-1)^{3}-3(-1)^{2}+2}{6(-1)^{2}-6(-1)}$
$x_{2}=-1+\frac{3}{12}$
$x_{2}=-0.75$
$x_{3}=-0.75-\frac{2(-0.75)^{3}-3(-0.75)^{2}+2}{6(-0.75)^{2}-6(-0.75)}$
$x_{3}=-0.75+0.0675$
$x_{3}=-0.6825$
