Newton

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%             -------------                             --------
%             function file                             newton.m
%             -------------                             --------

	function  [x] = newton(x1,epsilon)

    %==========================================================
     format long
     x=[];
     max=50;
	 x(1) = x1;
          
     for k=2:max
         fxAnt = (x(k-1))^5 + (-10/9)*(x(k-1))^3 +(5/21)*x(k-1);
         
         %   Derivada da funcao
         dfxAnt = 5*(x(k-1))^4 + 3*(-10/9)*(x(k-1))^2 +(5/21);
         
         %	Nova Aproximacao de Newton
	     x(k)  =  x(k-1) - ( fxAnt / dfxAnt );
         
         fxk = (x(k))^5 + (-10/9)*x(k)^3 +(5/21)*x(k);
         
         errox=abs(x(k)-x(k-1));
         
         errof=abs(fxk);
        
         if (errox < epsilon) | (errof < epsilon)
             break
         end    
     end
     %==========================================================