求函数f(x)=(x+5)(x+2)/(x+1) （x

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求函数f(x)=(x+5)(x+2)/(x+1)（x求函数f(x)=(x+5)(x+2)/(x+1)（x求函数f(x)=(x+5)(x+2)/(x+1)（xf(x)=(x+5)(x+2)/(x+1)=

求函数f(x)=(x+5)(x+2)/(x+1) （x
求函数f(x)=(x+5)(x+2)/(x+1) （x

求函数f(x)=(x+5)(x+2)/(x+1) （x
f(x)=(x+5)(x+2)/(x+1)
= (x+2)*[(x+1) + 4]/(x+1)
= (x+2)*[1 + 4/(x+1)]
= (x+2) + 4(x+2)/(x+1)
= (x+2) + 4[(x+1) + 1]/(x+1)
= (x+2) + 4[1 + 1/(x+1)]
= (x+2) + 4 + 4/(x+1)
= (x+1) + 4/(x+1) + 5
= -[-(x+1) - 4/(x+1)] + 5
x < -1,-(x+1) > 0 ,所以
-(x+1) + 4/[-(x+1)] ≥ 2 √[-(x+1)] * √[-4/(x+1)] = 4
-[-(x+1) - 4/(x+1)] ≤ -4
原式 ≤ -4 + 5 = 1
原式最大值为 1.
当 (x+1) = 4/(x+1) 时,取得最大值.,即
(x+1)^2 = 4,
x+1 = -2
x = -3

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