Consider the equation x = x - f(x) /f'(x) and sup-pose that f'(x) 0 in an

Question:

Consider the equation x = x - f(x) /f'(x) and sup-pose that f'(x) ≠ 0 in an interval [a, b].
a. Show that if r is in [a, b] then r is a root of the equation x = x - f(x) /f'(x) if and only if f (r) = 0.
b. Show that Newton's Method is a special case of the Fixed-Point Algorithm, in which g'(r) = 0.