答：
2<=x<=3
3<=x+1<=4
y=x²/(x+1)
=(x+1-1)²/(x+1)
=(x+1)-2+1/(x+1)
>=2√[(x+1)*1/(x+1)]-2
=2-2
=0
當(dāng)且僅當(dāng)x+1=1/(x+1)即x+1=1即x=0時取得最小值
x+1>1時y是x+1的單調(diào)遞增函數(shù)
所以：
x+1=3即x=2時取得最小值y(2)=4/(2+1)=4/3
x+1=4即x=3時取得最大值y(3)=9/(3+1)=9/4不好意思，打錯了，應(yīng)該是求函數(shù)最值：y=x^2/x-1,x∈【2,3】方法類似，自己求吧y=x²/(x-1)=(x-1+1)²/(x-1)=(x-1)+2+1/(x-1)>=2+2=4x-1=1/(x-1)即x-1=1即x=2時取得最小值4x=3時y取得最大值9/(3-1)=9/2