曲线y=1x-x在点P(4,-74)处的切线方程是()A.5x+16y+8=0B.5x-16y+8=0C.5x+16y-8=0D.5x-16y-8=0-数学

题目简介

曲线y=1x-x在点P(4,-74)处的切线方程是()A.5x+16y+8=0B.5x-16y+8=0C.5x+16y-8=0D.5x-16y-8=0-数学

题目详情

曲线y=
1
x
-
x
在点P(4,-
7
4
)处的切线方程是(  )
A.5x+16y+8=0B.5x-16y+8=0C.5x+16y-8=0D.5x-16y-8=0
题型:单选题难度:中档来源:不详

答案

∵y=class="stub"1
x
-
x

∴y'=-class="stub"1
x2
-class="stub"1
2
x-class="stub"1
2

∴y=f(x)在点P(4,-class="stub"7
4
)处的切线斜率是k=-class="stub"5
16

∴曲线y=f(x)在点P(4,-class="stub"7
4
)处的切线方程为:y+class="stub"7
4
=-class="stub"5
16
(x-4),
即5x+16y+8=0.
故选A.

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