y=3cosx-cos(2x)
=3cosx-(2cos²x-1)
=-2cos²x+3cosx+1
=-2(cosx-3/4)²+1+9/8
=-2(cosx-3/4)²+17/8
∵ cosx∈[-1,1]
则cosx=3/4时,y有最大值17/8
cosx=-1时,y有最小值-4