－4≤x≤－1時(shí),－4≤y≤－1,∴k=4.
設(shè)M(m,4/m),N(n,4/n),m>0>n,m+n≠0,
OM=√[m^2+(4/m)^2]>=√（2m^2*16/m^2)=2√2,當(dāng)m=土2時(shí)取等號(hào),
同理ON|min=2√2.
下面用導(dǎo)數(shù)求w=MN^2=(m-n)^2+(4/m-4/n)^2=(m-n)^2*[1+16/(mn)^2]的駐點(diǎn)坐標(biāo)：
w’m=2(m-n)[1+16/(mn)^2]-32(m-n)^2/(m^3n^2)=0,
化簡得m^3n^2+16m-16(m-n)=0,m^3n=-16,
同理由w’n=0得n^3m=-16.
解得m=2,n=-2,這時(shí)w=32,|MN|=4√2.
∴△MNO的周長L=OM+ON+MN>8√2,為所求.