题目内容
曲线y=

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A.

B.
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C.

D.

【答案】分析:由题意易知,点T为切点,故根据导数的几何意义,可得切线的方程,从而求出切线与两坐标轴的截距,故切线与两坐标轴围成的三角形的面积可求.
解答:解:由题意易知,点T为切点,
∵f′(1)=2,
∴切线方程为:y=2x-
,
∴它在两坐标轴的截距分别为
,-
,
∴与两坐标轴围成的三角形面积S=
×
×|-
|=
.
故选D.
点评:本题考查了导数的几何意义,主要用于解决切线问题.
解答:解:由题意易知,点T为切点,
∵f′(1)=2,
∴切线方程为:y=2x-

∴它在两坐标轴的截距分别为


∴与两坐标轴围成的三角形面积S=




故选D.
点评:本题考查了导数的几何意义,主要用于解决切线问题.

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