Question

求函数f(x)=-(log(0.5)x)²-log(0.25)x+5在[2,4]范围内的最值，并求出相应的x的值

Answer 1

f(x)=-(log(0.5)x)²-0.5*log(0.5)x+5。换元，令t=log(0.5)x,t 属于【-2，-1】，f(t)=-(t)²-0.5*t+5,现在求方程最值。求出t的值，在根据t=log(0.5)x，求出x的值。