求函数f(x)=(log2^x/4)log2^x/2)的最小值

问题描述:

求函数f(x)=(log2^x/4)log2^x/2)的最小值

f(x)=(log2^x/4)*(log2^x/2)
log2^x/2=log2^[(x/4)*2]=(log2^x/4)+1
f(x)=(log2^x/4)^2+(log2^x/4)=[(log2^x/4)+(1/2)]^2-(1/4)
当(log2^x/4)=(1/2),即x=4倍根号2时,f(x)取最小值负四分之一