Question

过曲线y=x－e^x上某点的切线平行于x轴,求这点的坐标及切线方程.

Answer 1

切线方程为y=－1.      

解析:

利用导数的几何意义,先求切点,再求切线的方程.

∵y′=1－e^x,                                                                                      3分

又切线与x轴平行,∴切线的斜率k=0.                                                        5分

∴令y′=1－e^x=0,得x=0.                                                                          7分

∴切点坐标为(0,－1).                                                                                8分

∴切线方程为y=－1.                                                                                 10分