Question

函数f(x)=ln(x+1)-a/x在区间(2,3)上有零点,则a的取值范围？

Answer 1

f(x) = ln(x+1) - a/x 在区间 (2, 3)上有零点, 则
f(2)f(3) = (ln3-a/2)(2ln2-a/3) = a^2/6 - (ln2+ln3/3) + 2ln6 < 0
a^2 - (6ln2+2ln3) + 12ln6 < 0
(a-6ln2)(a-2ln3) < 0, 2ln3 < a < 6ln2