2.求函数y=3sin²x-4sinx+1 x属于【-π/6,π/6】的值域

令t=sinx因为x∈【-π/6,π/6】所以t=sinx∈【-1/2,1/2】故y=3t²-4t+1=3(t-2/3)²+1-4/3=3(t-2/3)²-1/3所以当t=-1/2时,y取得最大值y=3(-1/2-2/3)²-1/3=15/4当x=1/2时,y取得最小值y=3(1/2-2/3)
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