哪个是曲线Y=x/x+2在点(-1,-1)处的切线方程?是Y=2x+1还是Y=-2x-3?

题目

哪个是曲线Y=x/x+2在点(-1,-1)处的切线方程?是Y=2x+1还是Y=-2x-3?

答案

y=x/(x+2)=(x+2-2)/(x+2)=1-2/(x+2)
求导y'=2/(x+2)^2
切线斜率K=y'=2/(-1+2)^2=2
方程y+1=2(x+1),即y=2x+1