已知函数f(x)=(x^2-ax+a)/x,x∈[1.+∞) (1)当a=4时,求函数f(x)的最小值若对任意x∈[1.+∞) ,_数学解答

已知函数f(x)=(x^2-ax+a)/x,x∈[1.+∞) (1)当a=4时,求函数f(x)的最小值
若对任意x∈[1.+∞) ,f(x)>0恒成立,试求实数a的取值范围

人气：225 ℃　时间：2020-07-02 15:49:42

解答

(1) when a = 4f(x) = (x-2)^2 / xwhen x = 2,f(2) = 0,which is minimum(2) f(x) = [(x-a/2)^2 + a - a^2/4]/xif f(x) > 0we must have (x-a/2)^2 + a - a^2/4 > 0when x = a/2 its minimum is a-a^2/4 which must ...