已知x滿足不等式2(log1/2 x)^2+7log1/2 x+3≤0.f(x)=(log2 x/4)^2(log2 x/2) 求函數(shù)的最大值和最小值
第一個(gè)式子在網(wǎng)上搜了一下
2(log1/2x)^2+7log1/2x+3≤0,
令,t=log1/2(x),有
2t^2+7t+3≤0,
(2t+1)(t+3)≤0.
-3≤t≤-1/2.
當(dāng)t=-3時(shí),log1/2(x)=-3,x=(1/2)^-3=8.
當(dāng)t=-1/2時(shí),log1/2(x)=-1/2,x=(1/2)^(-1/2)=√2.
∵log1/2(x),是減函數(shù),有
√2≤X≤8.
又∵log2(x)為增函數(shù),
∴當(dāng)X=√2時(shí),f(x)有最小值,
請(qǐng)?jiān)谠敿?xì)一點(diǎn)
∵log1/2(x),是減函數(shù)
,有 √2≤X≤8.
又∵log2(x)為增函數(shù),
∴當(dāng)X=√2時(shí),f(x)有最小值,
我認(rèn)為log1/2(x),是減函數(shù) X=8.時(shí)有最小值-3.X=√2時(shí)有最大值-1/2
第二道完全不會(huì)