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一次除以二次的最值怎么求

更新时间: 2020-11-12 00:00:00     

可以利用换元法,把它化作一元二次方程,再求最值

例如f(t)=(-1-t)/t2求最值

原式=-(1/t2+1/t)

令1/t=x,则x属于(负无穷,0)并上(0,正无穷)

所以原式=-x2-x=-(x2+x)=—(x+1/2)2+1/4

所以当x=-1/2时,即t=-2时,原式取最大值1/4

要注意换元后,变量的取值范围的变化

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