Analyze convergence of Newton's method for finding roots 
for the problem shown in class, f(x) = x^2*Exp[-x^2].  
Plot |x(n) - x(n-1)| as  a function of n. You can write your own code or use Mathematica. Your choice. Plot axes must be clearly labelled, everything should look nice 
and clearly visiable. 

(a) First, for when the
method converges nicely, for x0 = 0.2.  You can consider n <=10. 

(b) For the runaway problem example: 

FindRoot[x^2*Exp[-x^2], {x,  1.2}, Method -> Newton]