(2023新高考Ⅰ,19)已知函数. (1)讨论的单调性; (2)证明:当时,.
(2023新高考Ⅰ,19)已知函数.
(1)讨论的单调性;
(2)证明:当时,.
解:(1),
若,
则,;
令,得,
当,,
(2)由(1)可知,当时,
,
故只需证:,
即证:.
令,则
当,,;
故,证毕.