Ƒ(x) that is infinitely differentiable can be written as below Here h would be a small value that can be positive or negative. We have to keep on repeating the above step till we get really close toĪlternate Explanation using Taylor’s Series: We know that slope of line from (x 1, f(x 1)) to (x 2, 0) is f'(x 1)) where f’ represents derivative of f.īy finding this point 'x2', we move closer towards the root. Calculate f(x 2), and draw a line tangent at x 2. The point where the tangent line crosses the x axis should be a better estimate of the root than x 1. The idea is to draw a line tangent to f(x) at point x 1.
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