Question

函数f(x)=sin²x+根号3 sinxcosx在区间【π/4,π/2】上的最大值是

我得根号3

Answer 1

f(x)=sin²x+√3sinxcosx
=(1-cos2x)/2+(√3/2)sin2x
=(√3/2)sin2x-(1/2)cos2x+1/2
=sin(2x-π/6)+1/2

x∈[π/4,π/2]
π/3≤2x-π/6≤5π/6

所以f(x)的最大值是1+1/2=3/2

Answer 2

f(x)=sin²x+根号3 sinxcosx
=1/2-1/2cos2x+根号3/2*sin2x
=sin(2x-π/6)+1/2
x∈【π/4,π/2】 2x-π/6∈【π/3,5π/6】
所以当2x-π/6=π/2时,最大值是=1+1/2=3/2