已知二次函数f(x)=ax^2+(a-1)x+a 函数g(x)=f(x)+(1-(a-1)x^2)/x在(2,3)上是增
已知二次函数f(x)=ax^2+(a-1)x+a 函数g(x)=f(x)+(1-(a-1)x^2)/x在(2,3)上是增函数,求a的取值范围
g(x)=f(x)+[1-(a-1)x^2]/x
=ax^2+(a-1)x+a+[1-(a-1)x^2]/x
=[ax^3+(a-1)x^2+ax+1-(a-1)x^2]/x (含x^2项被合并同类向后约去)
=(ax^3+ax+1)/x
=ax^2+a+1/x
根据题意g'(x)=2ax-1/(x^2)≥0 在(2,3)上恒成立
∵2