




When does this method fail?
1. It must fail to solve f(x)=0 if that equation has no solutions!_{ }(the procedure will wander all over the place!)
2. If you happen to be on a point at which f'(x) is near zero, you fly away very far. Thus, when f(x)=0 has several solutions, you may not come across the closest solution to your starting point._{ }
3. If the second derivative of your function has the same sign between your start and the solution, you definitely will succeed.
4. If your function has a square root or other inverse function whose domain is restricted, Newton's method can make x_{k}a point on which f is undefined. It will then fail.