函数f（x）=sin2x+sinxcosx+1的最小正周期是，最小值是．

Question

函数f（x）=sin²x+sinxcosx+1的最小正周期是___，最小值是___．

Answer 1

∵f（x）=sin²x+sinxcosx+1
=(1-cos2x)/(2)+(1)/(2)sin2x+1
=(√(2))/(2)sin（2x-(π)/(4)）+(3)/(2)．
∴最小正周期T=(2π)/(2)=π，最小值为：(3)/(2)-(√(2))/(2)=(3-√(2))/(2)．
故答案为：π，(3-√(2))/(2)．