Question

急一道高一数学函数题,F（X）=（AX+1）/（X+2）在区间（-2,+无穷大）是增函数,求A的取值范围.急

Answer 1

F（X）=（AX+1）/（X+2）=(1-2A)/(x+2)+A

又因为在区间（-2,+无穷大）是增函数,则(1-2A)/(x+2）在区间（-2,+无穷大）单调增

所以1-2A1/2

A>1/2

或者利用高二学的求导

F（X）=（AX+1）/（X+2）=(1-2A)/(x+2)+A

即F'(x)=(2A-1)/[(x+2)^2]在区间（-2,+无穷大）上恒为正

则2A-1>0,得A>1/2