Question

已知函数f(x)=x方+ax-lnx 若函数f(x)在[1,2]上是减函数,求实数a的取值范围

Answer 1

2. g(x)=f(x)-x^2 = ax-lnx

=> g'(x)=a-(1/x)

=> 当x属于(0,e]时,g'(x)是增函数

=> g'(x) g(x)>=g(e)=ae-1 ,函数g(x)的最小值是3

=> ae-1 = 3

=> a = 4/e

(2)、当a>e时： 当x∈(0,1/a] =>g(x)是减函数

当x∈(1/a,e] =>g(x)是增函数

=> g(x)>=g(1/a)=1-ln(1/a) =3

=> ln(1/a) = -2

=> a = e^2