Question

函数y=log1/2(x+1(/x-1)-1)(x＞1)的最大值是

Answer 1

x＞1

y = log 1/2 {x+1/(x-1)-1)}

= log 1/2 {(x-1) +1/(x-1)}

∵x-1＞0

∴(x-1) +1/(x-1) = {根号(x-1) - 1/根号(x-1) }^2 + 2 ≥ 2

∵底数1/2 ＜1

∴当真数(x-1) +1/(x-1)取最小值时,y取最大值

∴ymax = log 1/2 2 = -1