Let x2 = a and f(x) = x2 – a. Here we know the root exactly, so we can see better how well the method converges.
This relation is known as Newton's iteration equation.
⁕ When the Newton's Method go wrong?
↪ Newton's method stops if f '(xn) = 0 at some level of iteration. Then the method has to be started with another initial guess.
⁕ Drawbacks of Newton Raphson's Method
↪ Divergent at inflection points
↪ Initial guess cannot be a point at which first derivative is zero.
↪ Oscillation near local maximum and minimum.