3. Root-Finding II

Newton’s Method — Quiz

Test your understanding of newton’s method with 5 practice questions.

Practice Questions

Question 1

Which formula gives the Newton iteration for solving $f(x)=0$?

Question 2

In Newton's method, the next approximation $x_{n+1}$ is the $x$-intercept of which line?

Question 3

If $f(x)=x^2-2$ and $x_0=1$, what is $x_1$ after one Newton step?

Question 4

Why can Newton's method fail at a current iterate $x_n$ when $f'(x_n)=0$?

Question 5

Which condition is a common stopping rule for Newton's method when successive iterates are changing very little?