已知函数f(x)=aInx+ 2/(x+1) (a∈R).(1)当a=1时,求f(x)在x∈[
问题描述:
已知函数f(x)=aInx+ 2/(x+1) (a∈R).(1)当a=1时,求f(x)在x∈[
已知函数f(x)=aInx+ 2/(x+1) (a∈R).
(1)当a=1时,求f(x)在x∈[1,+∞)上的最小值 (2)若f(x)存在单调递减区间,求a的取值范围
答
f(x)=aInx+2÷(x+1)(a∈R)a=1f(x)=Inx+2÷(x+1)(a∈R)f'(x)=1/x+(-2)/(x+1)²f'(x)=1/x-2/(x+1)²1/x-2/(x+1)²>0单调递增x/x²-2/(x+1)²>0[x(x+1)²-2x²]/x²(x+1)²>0x+...f'(x)=a/x+(-2)/(x+1)²f'(x)=a/x-2/(x+1)²a/x-2/(x+1)²=2根号a,,所以有2倍根号a根号5/2+3/2或a