已知x满足不等式2(log 1/2x) +7log1/2x+3≤0,3Q
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已知x满足不等式2(log 1/2x) +7log1/2x+3≤0,3Q
已知x满足不等式2(log 1/2x) +7log1/2x+3≤0,求函数f(x)=(log2四分之x)*(log2二分之x)的最大值和最小值
已知x满足不等式2(log 1/2x) +7log1/2x+3≤0,求函数f(x)=(log2四分之x)*(log2二分之x)的最大值和最小值
设T=log(1/2)(x) 则有:2T^2+7T+3<=0 (2T+1)(T+3)<=0 则:-3=<T<=-1/2 即:-3=<log(1/2)(x)<=-1/2 故:X属于[√2,8] f(x) =[log2(x/4)]*[log2(x/2)] =[log2(x)-log2(4)]*[log2(x)-log2(2)] =[log2(x)-2]*[log2(x)-1] =[log2(x)]^2-3[log2(x)]+2 =[log2(x)-3/2]^2-1/4 由于:X属于[√2,8] 则:log2(x)属于[1/2,3] 则:当log2(x)=3/2时 f(x)取最小值为-1/4 当log2(x)=3时 f(x)有最大值=2
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