Practice question · Select all that apply
Which statements about Newton's method are true?
Hints
- The method is fast when it works, but it is not guaranteed to work.
- Consider what happens when the tangent at your guess is horizontal.
Show the answer
- A. It can fail if the initial guess is far from a root
- B. Each step uses the formula ₊₁ = − f()/f'()
- D. It requires f'() ≠ 0 at each step
Why
Newton's method is not guaranteed to converge; a poor initial guess or a zero derivative causes failure.
Practise Graphs, approximation, and numerical sense
The app has 6 more questions on this lesson, and keeps your place in the course. Physics I is free to start.
More questions on Graphs, approximation, and numerical sense
- Newton’s method races to a root when it works, but pick the starting point badly and it fails. Which…
- The linearization L(x) = f(a) + f'(a)(x-a) is exact for every function on a small enough interval.
- Use linearisation to estimate sin(0.1). (Use sin(0) = 0 and cos(0) = 1.) Set the slider to your answer.
- A linear approximation is excellent near the expansion point and poor far from it. Why does the approximation…
- Order the steps in one iteration of Newton's method for root-finding.
- Use the linear approximation at x=16 to estimate √(16.4), then set the slider. (f(x)=√(x), f'(x) =…