设a属于R,函数f(x)=-(x-1)^2+2(a-1)ln(x+1)
2个回答

(1)

求导数:f片x=-2(x-1)+2(a-1)/(x+1)

当x=0时,f片x=-2(0-1)+2(a-1)/(0+1)=2a

可知此时的2a即为切线方程y=4x-1的斜率:2a=4

a=2

(2)f片x=-2(x-1)+2(a-1)/(x+1)

=【-2(x-1)*(x+1)+2(a-1)】/(x+1)

=2(a-x²)/(x+1)

又f(x)的定义域:x+1>0,x>-1

如果,a