BY USING SPUDER (PYTHON)

Basin of attraction

If x is a root of the function f(x), and f is dierentiable, then it is guaranteed that if Newtons method is initialized with x0 close to x, that the method will converge to x. The set of values for x0 for which Newtons method converges to x is called the basin of attraction for the root x.

i) Plot the function f(x) = 1 1+(x+1)2 + 1 100ex 0.5 on the domain [5,5] and verify that f has three roots.

ii) Find each of these roots to 10 d.p. iii) Run Newtons method, initializing with many dierent values of x0, and make a plot of the output of Newtons method vs initial value x0, where x0 ranges over [5,5]. Based on this plot, determine the basin of attraction for the middle of these three roots.