Newton’s method replaces a curve locally by its tangent and takes that tangent’s root as the next estimate. For , this gives , converging rapidly from the positive start shown.牛顿法在局部用切线代替曲线，将切线的零点作为下一次估计。对 ，更新为 ，从图中的正初值出发会快速收敛。
The gold tangent starts at each green point on the parabola. Its intersection with the horizontal axis becomes the next input; the iterations approach .金色切线经过抛物线上的绿色点，与横轴的交点成为下一次输入。各次迭代逐渐接近 。