Some curves are so flat that, in practice, Newtons method stops too far from the root to give a useful estimate Try Newtons method on (x) (x 1) 40 with a starting value of x 0 2 to see how close your machine comes to the root x 1 See the accompanying graph Slope 40 1 0 y (x 1)40 Nearly flat 1 2 Slo...

Lets apply Newtons method to the function x x 140 starting with x0 2 x1 x0 fx0f ...

Some curves are so flat that, in practice, Newtons method stops too far from the root to

Question:

Some curves are so flat that, in practice, Newton’s method stops too far from the root to give a useful estimate. Try Newton’s method on ƒ(x) = (x - 1)⁴⁰ with a starting value of x₀ = 2 to see how close your machine comes to the root x = 1. See the accompanying graph.