$($b$)$ Develop a matlab code to implement Newton's method.

Algorithm: $($Exactly as given in the textbook$)$

START PROGRAM

INPUT$/$INITIALIZATION : Input approximation $p_o$; Tolerance TOL;

maximum number of iterations $N_o.$

OUTPUT : Approximate Solution $p$ or message of failure.

STEP $1$ Set $i=1.$

STEP $2$ While $i{N}_o$ repeat Steps $3-6$ :

STEP $3$ Set $p=p_o-f\frac{p_o}{f^{\text{'}}}(p_o).$ Compute $p_i$

STEP $4$ If $i=i+1p_o=p{p}_o{N}_o{N}_o={?}^{\text{'}},N_o|p-p_o|$ then

OUTPUT $(p)$ the procedure was successful

STOP

STEP $5$ Set $i=i+1.$

STEP $6$ Set $p_o=p.$ Update $p_o$

STEP $7$ OUTPUT $(\text{'}$ The method failed after $N_o$ iterations, $N_o={?}^{\text{'}},N_o)$;

The procedure was unsuccessful.

END PROGRAM