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...ons to find the root of a real valued function f , i.e. a number x for which f (x) = 0, are of the form Example. To find the square root of a positive number y we can use Newton¡¯s method to solve the equation f (x) = x^2 - y = 0. Since f '(x) = 2x we see that Global Convergence. Does Zangwill¡¯s Theorem apply in this example ? What follows from it ? We can also use simple calculations here. Show that, if we start with x(0) > 0, for all k > 0 and for all k > 0. This implies the sequence decreases monotonically and converges to from any (positive) starting point. Spee...