已知x滿足根號2≤x≤8,求f(x)=(log(2)x/4)(log(2)x/2)的最大值與最小值
已知x滿足根號2≤x≤8,求f(x)=(log(2)x/4)(log(2)x/2)的最大值與最小值
數(shù)學(xué)人氣：999 ℃時(shí)間：2020-03-12 17:14:07
優(yōu)質(zhì)解答
f(x)=log2(x/4)×log2(x/2)
=[log2(x)-log2(4)]×[log2(x)-log2(2)]
=[log2(x)-2]×[log2(x)-1]
令t=log2(x)
∵x∈[2,8]
∴t=log2(x)∈[1,3]
f(x)=(t-2)(t-1)=t²-3t+2=(t-3/2)²-1/4
∵t=3/2在區(qū)間[1,3]內(nèi)
∴fmin=f(t=3/2)=-1/4
fmax=f(t=3)=2
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