So what are you using for f(x) and f'(x)? Can you show me at least one iteration of what you've been trying so I can see where you went wrong?
I need help on a Newton's Method problem. I have to "Use Newton's method to approximate the given number correct to eight decimal places".
The number is the hundredth root of 100 (100^(1/100)). When done on calculator, the result is 1.04712855. I've tried the approximation but am not able to get close.
The method is Xn+1=Xn-(f(n)/f'(n))
You can see that a guess of 1 or 2 won't get close after 9 iterations. 1.5 is much closer and 1.1 gets very close. So I guess the point of this is you have to make an approximation without a calculator, so using 1.1 needs to come from somewhere. If you graph the equation you can see that it's just above 1. Did your teacher make restrictions on how close your initial guess could be?
We have no restrictions on how to look for n. The only thing the professor said was to try using the Intermediate Value Theorem to "have an idea" of where the root or zero is located.
I guess the best number on this case is 1.1 indeed.
Thanks for your help and for the very useful site.
The formula is easy to follow but like I said just make sure you get a good starting guess so you don't go crazy doing the iteration 100 times.