证明:y=x+4/x在(-∞,-2)上单调递增

x1,x2∈(-∞,-2) x1>x2
f(x1)-f(x2)
=(x1+4/x1)-(x2+4/x2)
=(x1-x2)+4(x2-x1)/(x1x2)
=(x1-x2)(1-4/(x1x2))
[x1>x2 x1-x2>0
因为x1x2>(-2)^2=4 所以4/(x1x2)0]
>0
即y=x+4/x在(-∞,-2)上单调递增