已知函数f(x)=e^x\x-1当a=1时求曲线fx在（0,f(0))处的切线方程

Question

已知函数f(x)=e^x\x-1 当a=1时求曲线fx在（0,f(0))处的切线方程

Answer 1

如果题目是：已知函数f(x)=e^x\x-1 求曲线fx在（0,f(0))处的切线方程
则当x = 0时f(x) = 1/(0-1) = -1
因为f(x) = e^x/ (x-1)
所以f ' (x) =[ e^x (x-1) - e^x ]/(x-1)² 所以f ' (0) = [1 * (0-1) - 1 ]/(0-1)² = -2
所以过点（0,-1）斜率是-2的直线是：
y = -2x -1
即：曲线fx在（0,f(0))处的切线方程是:y = -2x -1