Bluewolf1986
New member
- Joined
- Sep 15, 2019
- Messages
- 17
Here's a question from my Calculus 1: Differential Calculus course on the Newton's Method Unit:
Find the largest interval around each of the roots x−x3=0 such that Newton's method converges to that root for every initial guess x0 in that interval.
(Enter answer as an interval (a, b). Enter infty for ∞ and -infty for −∞. Use round parentheses. You may type sqrt(2) for 2–√ etc. Type ∗ for multiplication, / for division, and ∧ for exponentiation.)
1) I got the first two answers right that the root around x=1 the interval is (sqrt(1/3), infinity) and around x=-1 the interval= (-infinity,-sqrt(1/3)
2) I need help with the root around x=0, I came up with (-sqrt(1/3), 0) but it was incorrect. I am stuck on how to contrive this interval. Please provide hints or methods to help me find this interval.
Thank you!
Find the largest interval around each of the roots x−x3=0 such that Newton's method converges to that root for every initial guess x0 in that interval.
(Enter answer as an interval (a, b). Enter infty for ∞ and -infty for −∞. Use round parentheses. You may type sqrt(2) for 2–√ etc. Type ∗ for multiplication, / for division, and ∧ for exponentiation.)
1) I got the first two answers right that the root around x=1 the interval is (sqrt(1/3), infinity) and around x=-1 the interval= (-infinity,-sqrt(1/3)
2) I need help with the root around x=0, I came up with (-sqrt(1/3), 0) but it was incorrect. I am stuck on how to contrive this interval. Please provide hints or methods to help me find this interval.
Thank you!