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?

来源:学生作业帮助网 编辑:作业帮 时间:2024/09/28 06:40:37
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?
x){:yՓXlGVWh=yN ]C]CͧKZjy6m@Fچ/u*tml~ -\Y 4Bh-5҄ u ,gSn 3xj˜}޶i]C-DچF@:O{7Wb_\g p @PmTZ E0 p a~O== 3e1Vl,Э`4:h0O"^DdRzx,0nY

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?
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?

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?
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

y=x/(x+2)=1-2/(x+2)
y'= 2/(x+2)^2
y'(-1)= 2/(-1+2)^2=2
曲线 y=x/(x+2)在点(-1,-1)处的切线方程为:
y-(-1)=2(x-(-1) -->
y=2x+1

y=x/(x+2)
y'=[(x+2)-x]/(x+2)^2=2/(x+2)^2=2
所以
y+1=2(x+1)=2x+2
y=2x+1