求函数f(x)=(log1/4(x))^2+log1/4(x^2)+5 2≤x≤16,求最大值和最小值

求函数f(x)=(log1/4(x))^2+log1/4(x^2)+5 2≤x≤16,求最大值和最小值
求函数f(x)=(log1/4(x))^2+log1/4(x^2)+5 2≤x≤16,求最大值和最小值

求函数f(x)=(log1/4(x))^2+log1/4(x^2)+5 2≤x≤16,求最大值和最小值
2≤x≤16
log1/4(16)≤log1/4(x)≤log1/4(2)
-2≤log1/4(x)≤-1/2
令t=log1/4(x),则t∈[-2,-1/2]
f(t)=t²+2t+5=(t+1)²+4
f(t)的图象是开口向上的抛物线
抛物线的对称轴是t=-1
离对称轴越远,函数值越大
当t=-1时,f(t)取最小值f(-1)=4
当t=-2时,f(t)取最大值f(-2)=5
函数f(x)的最大值是5,最小值是4

现在做！

记log1/4(x)=t
t=log1/4(x)=-[lg2(x)]/2
1<=lg2(x)<=4
-2<=t<=-1/2
f(t)=t^2+2t+5=(t+1)^2+4
-1<=t+1<=1/2
0<=(t+1)^2<=1
4<=f(t)<=5
f(x)最大值5，最小值4.