已知x<4分之5,函数y=4x-2+4x-5分之1的最大值为
人气:354 ℃ 时间:2020-01-26 06:50:37
解答
x<5/4 即4x-5<0
y=4x-2+[1/(4x-5)]
=4x-5+[1/(4x-5)]+3
令4x-5为t,t<0,原式=t+(1/t)+3
=-[(-t)+(1/-t)]+3
又因为[(-t)+(1/-t)]≥2√[-t×(1/-t)]≈2
得:t+(1/t)≤-2 则原式=t+(1/t)+3≤1
故y=4x-2+[1/(4x-5)]≤1
当t=(1/t)=-1时,x=1有最大值为1
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