📝 Some Difficulties With Newton’s Method

Q1. When applying Newton's method to \(f(x)=x^{3}-2x+2\) with initial guess \(x_{0}=0\), what is the most likely behavior of the iterates?

💡 Difficulty: easy | ✅ Correct: A

Q2. A function \(f\) has a simple root at \(r\) and \(f'(r)=0.001\). How does this affect the speed of Newton's method near \(r\)?

💡 Difficulty: medium | ✅ Correct: B

Q3. A function \(f\) is defined by \(f(x)=x^{5}-x-1\). Which statement about Newton's method starting at \(x_{0}=0\) is correct?

💡 Difficulty: hard | ✅ Correct: A