已知函数f(x)=-2sin^2x+2根号3sinxcosx+1

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/13 21:31:55

已知函数f(x)=-2sin^2x+2根号3sinxcosx+1
若x属于[-π/6,π/3] 求f（x）的最大值和最小值

sin^2 X = 1/2 - (1/2)cos(2X))
so f(x) = -1 + cos(2x) + sqrt(3)sin2x + 1
= 2sin(2x+pi/6)
when x belongs to -pi/6,pi/3,
2x + pi/6 belongs to -pi/6 to 5pi/6
fmin = -0.5
fmax = 1

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