" the point x x, at which the Continui closer to the rootsfashion, we obtain a sequence of ang gure 2·s, is a better imation to the root r than xg- To improve the next estimate x (Figure 3) {Xy.X2·Xy. ..) that ideally get closer and s using x, to In general, after ri after n steps, the line tangent to the curve at x 4). In Steps 1 and 2 we derive a formula for fi is used to find an updated in terms of x, finding 1. Recall the point-slope form of the equation of a line of slope m passing through ()is Figure 4 y-yi = m (x-xi ) . Use this equation to verify that the line tangent to the curve y y = f(%)+ f'(%)(x-%). f(x) at x-h is
