【急】函数f(x)=sin²x+√3sinxcosx在区间{π/4,π/2},求f（x）最大值

【急】函数f(x)=sin²x+√3sinxcosx在区间{π/4,π/2},求f（x）最大值
【急】函数f(x)=sin²x+√3sinxcosx在区间{π/4,π/2},求f（x）最大值

【急】函数f(x)=sin²x+√3sinxcosx在区间{π/4,π/2},求f（x）最大值
f(x)=(1-cos2x)/2+根号3/2sin2x=1/2+sin(2x-π/6)
x∈【π/4,π/2】,2x-π/6∈【π/3,5π/6】,sin(2x-π/6)∈【1/2,1]
f(x)max=f(π/3)=3/2
f(x)min=f(π/2)=1