求函数y=-2cos^2x+2sinx+3,x∈[π/6,5π/6]的最大值和最小值.
人气：161 ℃ 时间：2019-08-19 18:26:40
解答
y=-2cos²x+2sinx+3=-2(1-sin²x)+2sinx+3=2sin²x+2sinx+1=2(sinx+1/2)²+1/2因为x∈[π/6,5π/6]所以sinx∈[1/2,1]所以函数的最大值是2(1+1/2)²+1/2=5,最小值是2(1/2+1/2)²+1/2=5/2...
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