Hi so I have been having some issues with Newton's Method. I understand what you have to do, however, I was solving this one equation, yet no matter what I did I could not arrive at the correct answer.

The question was to use Newton's method to approximate the real root of f(x)=2x^7-1 to 3 decimal places. I see x1=1 and when I do it I get 0.928571429. What I am supposed to get is 0.907343 as my x2. What do I do?

Also this one problem I cannot figure out at all. Use Newton's Method to find the value of squareroot7 until two consecutive terms of the sequence are within 0.0001. (Hint squareroot7 is a root of what function?) I'm very confused on this problem, any help is appreciated.

Edit I have fixed my error in the first problem, I was too stupid to not keep going. However, the second confuses me still, I've tried multiple methods to solve it but cannot come up with anything.

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