设x＞-1，求函数y＝(x+5)(x+2)x+1的最小值．

Question

设x＞-1，求函数y＝((x+5)(x+2))/(x+1)的最小值．

Answer 1

∵

y＝([(x+1)+4][(x+1)+1])/(x+1)＝x+1+(4)/(x+1)+5≥2√((x+1)(4)/(x+1))+5＝9(x+1＝(4)/(x+1)取等)

所以仅当x=1时，y_min=9．