Home | 18.01 | Chapter 9 | Section 9.1

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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 xka point on which f is undefined. It will then fail.