求函数y=2(log1/4底4x)^2+7log1/4底x+1,x∈【2,4】的最大值与最小值.

求函数y=2(log1/4底4x)^2+7log1/4底x+1,x∈【2,4】的最大值与最小值.
求函数y=2(log1/4底4x)^2+7log1/4底x+1,x∈【2,4】的最大值与最小值.

求函数y=2(log1/4底4x)^2+7log1/4底x+1,x∈【2,4】的最大值与最小值.
答：
y=2*[log1/4(4x)]^2+7log1/4(x)+1
=2*[log1/4(4)+log1/4(x)]^2+7log1/4(x)+1
=2*[-1+log1/4(x)]^2+7log1/4(x)+1 设m=log1/4(x),2

log1/4底4x=log1/4(4)+log1/4(x)=-1+log1/4(x)

令log1/4(x)=t

则y=2(t-1)^2+7t+1=2t^2+3t+3

t=log1/4(x)    x∈[2,4]

t∈[-1,-1/2]

t=-1时，最大值=2

t=-3/4时，最小值=15/8