Answer
$x_{3} = -1.29172$
Work Step by Step
$f(x) = x^7 + 4$
$f'(x) = 7x^6$
$x_{n+1}=x_{n}-\frac{x_n^7+4}{7x_n^6}$
$x_{1} = -1$
$x_{2} = -1 - \frac{-1^7 + 4}{7(-1^6)}$
$x_{2} = -1 - \frac{3}{7}$
$x_{2} = -1.42857$
$x_{3} = -1.42857 - \frac{-1.42857^7 + 4}{7(-1.42857)^6}$
$x_{3} = -1.42857 + 0.136853$
$x_{3} = -1.29172$
