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+//Newton's Method

+//the first few iteration converges quikcly in negative root as compared to positive root

+clc;

+clear;

+close();

+funcprot(0);

+format('v',9);

+deff('[Newton]=fx(x)','Newton=exp(x)-x-2');

+deff('[diff]=gx(x)','diff=exp(x)-1');

+x = linspace(-2.5,1.5);

+plot(x,exp(x)-x-2)

+//from the graph the function has 2 roots

+//considering the initial negative root -10

+x1 = -10;

+x2 = x1-fx(x1)/gx(x1);

+i=0;

+while abs(x1-x2)>(0.5*10^-7)

+    x1=x2;

+    x2 = x1-fx(x1)/gx(x1);    

+    i=i+1;

+end

+disp(i,'Number of iterations : ')

+disp(x2,'The negative root of the function is : ')

+

+

+//considering the initial positive root 10

+x1 = 10;

+x2 = x1-fx(x1)/gx(x1);

+i=0;

+while abs(x1-x2)>(0.5*10^-7)

+    x1=x2;

+    x2 = x1-fx(x1)/gx(x1);    

+    i=i+1;

+end

+disp(i,'Number of iteration : ')

+disp(x2,'The positive root of the function is : ')

+//number of iterations showing fast and slow convergent
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