f(x)=sinx/2*cosx/2+cos^2(x/2)-2求函数f(x)在[π,17/12π]上的最大值和最小值

f(x)=sinx/2*cosx/2+cos^2(x/2)-2求函数f(x)在[π,17/12π]上的最大值和最小值
f(x)=sinx/2*cosx/2+cos^2(x/2)-2求函数f(x)在[π,17/12π]上的最大值和最小值

f(x)=sinx/2*cosx/2+cos^2(x/2)-2求函数f(x)在[π,17/12π]上的最大值和最小值
f(x)=sinx/2*cosx/2+cos^2(x/2)-2
=1/2sinx+1/2(cosx+1)-2
=1/2(sinx+cosx)
=√2/2sin(x+π/4)
y=sinX在(π,3π/2)是减函数
π

f(x)=sinx/2*cosx/2+cos^2(x/2)-2
=(1/2)*2sinx/2*cosx/2+[2cos^2(x/2)-1]/2-3/2
=(1/2)*sinx+cosx-3/2
=√[(1/2)^2+1]*sin(x+arctan2)-3/2
=√5/2*sin(1*x+arctan2)-3/2
∴函数f(x)的最小正周期是2π/1=2π