函数f(x)=cosx+根号3sinx(0＜=x＜=π/2）f （x）的最小值是?
问题描述：
函数f(x)=cosx+根号3sinx(0＜=x＜=π/2）f （x）的最小值是?
答
f(x)=√3sinx+cosx
=2(√3/2sinx+1/2cosx)
=2sin(x+π/6)
0≤x≤π/2
π/6≤x≤2π/3
sint在π/6≤x≤2π/3[],先增后减,
1/2≤sin(x+π/6)≤1
1≤2sin(x+π/6)≤2
f(min)=1