### 1. 泰勒展开公式（牛顿法）

$$\varphi (x)=\frac{f(x_0)}{0!}+\frac{f'(x_0)}{1!}(x-x_0)+\frac{f''(x_0)}{2!}(x-x_0)^2+...+\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n$$

$$\varphi (x) \approx \frac{f(x_0)}{0!}+\frac{f'(x_0)}{1!}(x-x_0)+\frac{f''(x_0)}{2!}(x-x_0)^2$$ when $$\varphi'(x_0) = 0$$ $$f'(x_0)+f''(x_0)(x-x_0)=0$$ $$x=x_0-\frac{f'(x_0)}{f''(x_0)}$$