已知函数f(x)=(log1/2x）²-log1/4+5,x∈[2,4],求f(x)的最小值与最大值.

题目

已知函数f(x)=(log1/2x）²-log1/4+5,x∈[2,4],求f(x)的最小值与最大值.

答案

log1/2x=- log2x,log1/4 x=-1/2* log2x
f(x)=(log1/2x)^2-log1/4x+5
=(log2x)^2+1/2*log2x+5
设log2x=t
y=t^2+1/2t+5=(t+1/4)^2+79/16,1