已知函数f(x)=log3(x/27)*log3(ax).(1/27

题目

已知函数f(x)=log3(x/27)*log3(ax).(1/27<=x<=9)求f(x)的最小值

答案

f(x)=(log3x-log327)(log3a+log3x)
f(x)=(log3x-3)(log3a+log3x)
t=log3x
f(t)=(t-3)(log3a+t)
f(t)=log3at+t^2-3log3a-3t
f(t)=t^2+(log3a-3)t-3log3a
f(t)=(t-(log3a-3)/2)^2-(log3a-3)^2/4-3log3a
1/27