若π/4
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若π/4若π/4若π/4若π/4y=tan2x(tanx)^3=2(tanx)^4/(1-tan^2x)π/4tanx>=1t=tan^2x>=1y=2t^4/(1-t^2)=-[2(t^2-1)(t
若π/4 若π/4 建议：\x09 提示：如果调整效果始终不能满意，则可选择斜线表头框架，右击鼠标选择“取消组合”命令，将斜线表头框架打散重新调整各部分的位置，然后再将它们组合起来即可。 看图 Y=tan2X*tan³X
若π/4
若π/4<=x<π/2,则函数y=tan2x乘以(tanx)^3的最大值
y=tan2x (tanx)^3
=2(tanx)^4/(1-tan^2 x)
π/4<=x<π/2
tanx>=1
t=tan^2 x>=1
y=2t^4/(1-t^2)
=-[2(t^2-1)(t^2+1)+2]/(t^2-1)
=-2[(t^2+1)+1/(t^2-1)]
=-2](t^2-1)+1/(t^2-1)+2]
<=-2[2+2]
<=-8
当且仅当t=1, tanx=1,x=π/4时
y max=-8
＝2tan^4 x/(1-tan^2 x)
令t＝tan^2 x>1，
y=2t^4/(1-t^2)
=[2(t^2+1)(t^2-1)+2]/(1-t^2)
=-2(t^2+1)+2/(1-t^2)
=-2[(t^2-1)+1/(t^2-1)+2]
≤-2[2+2]
＝－8
当(t^2-1)＝1/(t^2-1)，t＝√2时，y max＝－8