函数y=(x^2+7x+22)/(x+1)(x
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函数y=(x^2+7x+22)/(x+1)(x
函数y=(x^2+7x+22)/(x+1)(x
函数y=(x^2+7x+22)/(x+1)(x
y=(x^2+7x+22)/(x+1)
=[(x^2+x)+(6x+6)+16]/(x+1)
=[x(x+1)+6(x+1)+16]/(x+1)
=x+6+16/(x+1)
=(x+1)+16/(x+1)+5
x=2√[(x+1)*16/(x+1)](利用基本不等式定理)
=2√[(x+1)*16/(x+1)]
=2*4
=8
(x+1)+16/(x+1)
原式=[(x+1)²+5(x+1)+16]/(x+1)=(x+1)+16/(x+1)+5
x<-1时,由均值不等式,得 (x+1)+16/(x+1)+5≤-2√16+5=-3
故 最大值为-3,此时x+1=16/(x+1),x=-5
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