有函数y=(x^2-x+4)/(x-1), x属于[2,3],求y范围
热心网友
解:y=[x(x-1)+4]/(x-1)=x +4/(x-1)=(x-1)+4/(x-1) +1≥2√[(x-1)*4/(x--1)] +1 =4+1=5,当且仅当x-1=4/(x-1)时取等号,此时x=3在[2,3]内,即x=3时,y有最小值5,又因y=x +4/(x-1)在[2,3]为减函数,故x=2时,y最大为6,所以当x∈[2,3]时,y∈[5,6]
热心网友
x(x-1)+4/x-1=x+4/(x-1)2<=4/(x-1)<=44<=y<=7