The roots of (x) 1 3x 3 4x 1 to three decimal places are 3 583, 0 251, and 3 332 (Figure 11) Determine the root to which Newtons Method converges for the initial choices x 0 1 85, 1 7, and 1 55 The answer shows that a small change in x 0 can have a significant effect on the outcome of Newtons Metho...

Let fx x 4x 1 and define Taking xo 185 we have n 1 558 n Taking xo 17 we ...

The roots of (x) = 1/3x 3 4x + 1 to three decimal places are 3.583,

Question:

The roots of ƒ(x) = 1/3x³− 4x + 1 to three decimal places are −3.583, 0.251, and 3.332 (Figure 11). Determine the root to which Newton’s Method converges for the initial choices x₀ = 1.85, 1.7, and 1.55. The answer shows that a small change in x₀ can have a significant effect on the outcome of Newton’s Method.

-3.583 4- -4 0.251 3.332/ -X