求函数y=2(log1/4底4x)^2+7log1/4底x+1,x∈【2,4】的最大值与最小值.
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求函数y=2(log1/4底4x)^2+7log1/4底x+1,x∈【2,4】的最大值与最小值.
求函数y=2(log1/4底4x)^2+7log1/4底x+1,x∈【2,4】的最大值与最小值.
求函数y=2(log1/4底4x)^2+7log1/4底x+1,x∈【2,4】的最大值与最小值.
答:
y=2*[log1/4(4x)]^2+7log1/4(x)+1
=2*[log1/4(4)+log1/4(x)]^2+7log1/4(x)+1
=2*[-1+log1/4(x)]^2+7log1/4(x)+1 设m=log1/4(x),2
log1/4底4x=log1/4(4)+log1/4(x)=-1+log1/4(x) 令log1/4(x)=t 则y=2(t-1)^2+7t+1=2t^2+3t+3 t=log1/4(x) x∈[2,4] t∈[-1,-1/2] t=-1时,最大值=2 t=-3/4时,最小值=15/8