题目

The Austrian capital, Vienna, has beaten Australia’s Melbourne to be named the world’s most livable city of 2018.It’s the first time a European city has topped the first of the Economist Intelligence Unit(EIU)annual survey.The worldwide league table ranks 140 cities on a range of factors, including political and social stability, crime, education and access to healthcare.In the survey, Manchester saw the biggest improvement of any. European city, rising by 16 places to rank 35th. Manchester’s rise puts it ahead of London in the rank by 13 places, the widest gap between the two cities s9．已知函数f（x）=ln$\frac{1}{2a{x}^{2}+bx+8a}$．（1）当a=$\frac{1}{4}$时，若函数f（x）为偶函数，求实数b的值；（2）当b=-3时，若函数f（x）在（4，+∞）上单调递减，求实数a的取值范围．