f（x）=﹣2sin的平方x+2根号3sinxcosx+1 =cos2x+(根号3）sin2x=2sin（2x+π/6）所以T=π,对称中心即f(x)=0,2sin（2x+π/6）=0,所以2x+π/6=kπ,得x=kπ/2-π/12x∈[-π/6,π/3]时,[-π/6,π/6]单增,[π/6,π/3]单减,...