第1个回答 2022-05-15
若曲线
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/562c11dfa9ec8a1332d8a574e503918fa1ecc060?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
的切线垂直于直线
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/a8ec8a13632762d0a4fc562bb2ec08fa503dc660?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
,试求这条切线的方程。
容易求
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/58ee3d6d55fbb2fb1ee9aa865d4a20a44723dc60?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
,因为切线垂直于直线
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/a8ec8a13632762d0a4fc562bb2ec08fa503dc660?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
,所以切线的斜率为
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/4e4a20a4462309f7f3ad5f86600e0cf3d6cad660?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
,令
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/21a4462309f79052fcddb5aa1ef3d7ca7acbd560?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
得
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/730e0cf3d7ca7bcb63b935bbac096b63f724a860?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
,所以切点的坐标为
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/f31fbe096b63f624059fcb979544ebf81b4ca360?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
,所以所求的切线的方程为
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/f7246b600c3387449a07dde8430fd9f9d62aa060?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
,即
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/908fa0ec08fa513d7e689e4a2f6d55fbb3fbd960?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
。
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