Question

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

x∈［－六分派，三分派］，求f(x)的值，并指出f(x)取得最值时x的取值

Answer 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