π/2≤x≤π/2时,函数y=sinx+根号3cosx的最大值,最小值,
问题描述:
π/2≤x≤π/2时,函数y=sinx+根号3cosx的最大值,最小值,
答
y=2(sinxcosπ/3+cosxsinπ/3)
=2sin(x+π/3)
x=π/6属于[-π/2,π/2],ymax=2
x=-π/2属于[-π/2,π/2],ymin=sin(-π/6)=-1/2