Question

设函数f(x)=2㏑(x+1)+x²/(x+1) (1)讨论函数f(x)的单调性；

Answer 1

1）f'(x)=2/(x+1)+[2x(x+1)-x²]/(x+1)²=(2x+2+x²+2x)/(x+1)²=(x²+4x+2)/(x+1)²

定义域为x>-1,

由f'(x)=0, 得x=-2+√2

单调增区间：x>-2+√2,

单调减区间：-1