已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),且x∈[0,π/2]求函数f(x)=a·b-4|a+b|的最小值
问题描述：
已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),且x∈[0,π/2]求函数f(x)=a·b-4|a+b|的最小值
答
a dot b=(cos(3x/2),sin(3x/2)) dot (cos(x/2),-sin(x/2))=cos(3x/2+x/2)=cos(2x)a+b=(cos(3x/2),sin(3x/2))+(cos(x/2),-sin(x/2))=(cos(3x/2)+cos(x/2),sin(3x/2)-sin(x/2))|a+b|^2=(cos(3x/2)+cos(x/2))^2+(sin(3x...