Page 86 - Calculus for the Clueless, Calc II

Find the root of f(x) = x - X - 3 using Newton's method. The graph in the figure was made using the fun TI 82
3
2
3
calculator, f(x) = x - x - 3. Therefore, f'(x) = 3x - 1.
Newton's formula becomes

Simplifying.......we get

f(1) = -3 and f(2) = 3.

Let us take x 1 = 1.5 for the first approximation. Probably x 1 = 1 or x l = 2 would work just fine.

Continuuuuing, we would get

We have reached the accuracy of our calculator: nine decimal places, which is probably more accurate than we
would ever need.

Note 1

Sometimes the method doesn't work. A full study is left to other courses.

Note 2

When it works, it usually works very quickly and with great accuracy.