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.](/uploads/image/z/2554190-62-0.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0y%3D2%28log1%2F4%E5%BA%954x%29%5E2%2B7log1%2F4%E5%BA%95x%2B1%2Cx%E2%88%88%E3%80%902%2C4%E3%80%91%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%8E%E6%9C%80%E5%B0%8F%E5%80%BC.)
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