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3. (5 分) 曲线 $y=\frac{x}{x+2}$ 在点 $(-1,-1)$ 处的切线方程为（ $）$

Gaokao · Math · previous-year question

  1. A.$y=2 x+1$correct
  2. B.$y=2 x-1$
  3. C.$y=-2 x-3$
  4. D.$y=-2 x-2$

Answer

A. $y=2 x+1$

Explanation

解: $\because y=\frac{x}{x+2}$, $\therefore y^{\prime}=\frac{2}{(x+2)^{2}}$ 所以 $\mathrm{k}=\left.\mathrm{y}^{\prime}\right|_{\mathrm{x}=-1}=2$, 得切线的斜率为 2 , 所以 $\mathrm{k}=2$; 所以曲线 $y=f(x)$ 在点 $(-1,-1)$ 处的切线方程为: $y+1=2 \times(x+1)$ ，即 $y=2 x+1$. 故选: A.

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