y=tan2xtan^3x
y=2tanx^4/(1-tanx^2)
=(2tanx^4-2+2)/(1-tanx^2)
=[2(tanx^2-1)(tanx^2+1)]/(1-tanx^2)+2/(1-tanx^2)
=-2(tanx^2+1)+2/(1-tanx^2)
=-2(tanx^2-1)+2/(1-tanx^2)-4
=－{[2(tanx^2-1)]+[2/(tanx^2-1)]}-4
π/4
上式≤－2{√[2(tanx^2-1)]*[2/(tanx^2-1)]}－4＝-8
当且仅当2(tanx^2-1)＝2/(tanx^2-1)时，即tanx=根号2时取等号
最大值为－8
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