已知函数f(x)=a(sin2X+cos2X),且f(π/4)=-1
问题描述:
已知函数f(x)=a(sin2X+cos2X),且f(π/4)=-1
(1)求a的值(2)求函数f(x)的最大值及取最大值时自变量x的集合(3)求函数f(x)的单调递增区间
答
1)f(x)=√2(sin2xcosπ/4+cos2xsinπ/4)+2a=√2sin(2x+π/4)+2a∴最小正周期T=2π/2=π2)、∵0≤x≤π/2∴π/4≤2x+π/4≤5π/4∴-√2/2≤sin(2x+π/4)≤1则f(x)min=√2*(-√2/2)+2a=2a-1=-2∴a=-1/2...