y=2cos2x-2acosx-2(2a+1)y=2[2(cosx)^2-1]-2acosx-4a-2y=4(cosx)^2-2acosx-4(a+1)令t=cosx,-1≤t≤1y=4t^2-2at-4(a+1)
-1≤t≤1对称轴:t=a/4,当-1<a/4<1,-4<a<4时,f(a)=[-64(a+1)-4a^2]/16=1/2-4(a+1)-a^2/4=1/216a+16+a^2+2=0a^2+16a+18=0解得:a=-8+√46(<0),a=-8-√46 (舍去)t=1时y有最大值48-6√46;a/4≥1, a≥4时,t=1有最小值-6a-6a=1/2,a=-1/12,... |