函数y=cosx-(1/2)cos2x(x∈R)的最大值最小值得和是
问题描述：
函数y=cosx-(1/2)cos2x(x∈R)的最大值最小值得和是
答
y=cosx-(1/2)cos2x=y=cosx-(1/2)cos^2x+(1/2)sin^2x=cosx-(1/2)cos^2x+(1/2)-(1/2)cos^2x
=cosx-cos^2x+1/2=-(cosx-1/2)^2+3/4最大值3/4最小值-3/2
最大值最小值得和-3/4
答
y=cosx-(1/2)cos2x
=cosx-(2cos^2x-1)/2
=cosx-cos^2x+1/2
=-(cosx-1/2)^2+1/2+1/4
=-(cosx-1/2)^2+3/4
cosx=1/2 最大值=3/4
cosx=-1 最小值=-3/2
和=3/4-3/2=-3/4