x=2時(shí),y=(4-8+13)/1=9
x=5時(shí),y=(25-20+13)/4=9/2
y=(x^2-4x+13)/(x-1)
y'=[(2x-4)(x-1)-x^2+4x-13]/(x-1)^2
=(x^2-2x-9)/(x-1)^2
=[(x-1)^2-10]/(x-1)^2
(x-1)^2<10時(shí),函數(shù)單調(diào)遞減,(x-1)^2≥10時(shí),函數(shù)單調(diào)遞增.當(dāng)(x-1)^2=10時(shí),函數(shù)取得最小值.
x=√10+1
ymin=(11+2√10-4-4√10+13)/√10
=(20-2√10)/√10
=2(√10-1)
函數(shù)的值域?yàn)閇2(√10-1),9]