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 Slope 40 (2, 1) X

Question: 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

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. Slope = -40 1 0 y = (x - 1)40 Nearly flat

Slope = -40 1 0 y = (x - 1)40 Nearly flat 1 2 Slope = 40 (2, 1) > X

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