Solve the Problem $h > 0$ , Applying Newton's Method To $$f ( x ) = \left\{ \begin{array} { l l } \sqrt { x - 8 } , & x \geq 8 \\- \sqrt { 8 - x } , & x < 8\end{array} \right.$$

Essay

Solve the problem.
-Show that if $h > 0$ , applying Newton's method to
$$f ( x ) = \left\{ \begin{array} { l l } \sqrt { x - 8 } , & x \geq 8 \\- \sqrt { 8 - x } , & x < 8\end{array} \right.$$
leads to $x _ { 2 } = h$ if $x _ { 0 } = h$ and to $x _ { 2 } = - h$ if $x _ { 0 } = - h$ when $0 < 8 < h$ .