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Home Limits, Analytic Geometry, and Approximations Newton's Method When to Use Newton's Method  
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When to Use Newton's Method
We wish to approximate a zero of f(x), where f'(x) is continuous and not close to zero, as in Figure 5.9.1.
As a rough check on the accuracy, compute f(x_{n}) and note how close it is to zero. Steps 3 and 4 can be done conveniently on a hand calculator. Warning: Since Newton's method involves division by f'(x_{1}) avoid starting at a point where the slope is near zero. Figure 5.9.3 shows that when the slope is close to zero, the tangent line is nearly horizontal and the approximation may be poor.
Figure 5.9.3


Home Limits, Analytic Geometry, and Approximations Newton's Method When to Use Newton's Method 