已知向量a=(根号3sinx,cosx),b=(cosx,cosx),函数f(x)=向量a*向量b

2025-04-14 21:45:57
推荐回答(1个)
回答1:

f(x)=a*b=√3sinxcosx+cos^2x
=√3/2sin2x+1/2cos2x+1/2
=sin(2x+π/6)+1/2

x∈[-π/6,π/3]
2x+π/6∈[-π/6,5π/6]
f(x)=sin(2x+π/6)+1/2在[-π/6,5π/6]上值域为:[0,3/2]
当x=-π/12时,f(x)有最小值=0
当x=π/6时,f(x)有最大值=3/2