题目

（本小题满分14分）设函数 （Ⅰ）当时，求的最大值； （Ⅱ）令，（），其图象上任意一点处切线的斜率≤恒成立，求实数的取值范围； （Ⅲ）当，，方程有唯一实数解，求正数的值． 答案：解：（Ⅰ）依题意，知的定义域为（0，+∞）， 当时，， （2′）令=0， 解得．（∵） 因为有唯一解，所以，当时， ，此时单调递增； 当时，，此时单调递减。 所以的极大值为，此即为最大值        ………5分 （Ⅱ），，则有≤，在上恒成立， 所以≥，              当时，取得最大值，所阅读理解阅读下面短文，简要回答所给问题。A long time ago,there was a big apple tree.A little boy liked playing around it every day.As the little boy grew up, he no longer played around the tree.One day the boy came back to the tree.He looked sad. “What’s troubling you?” asked the tree.The boy answered, “I want my own house. I need money to buy it.”“You can pick my apples and sell them. Then you will have money.”A few years later, the boy returned. He told the tree that he wanted to go sailing(航海) around the world.“Use my branches(树枝) to build your boat. You can sail far and be happy.” So the boy cut the branches to make a boat. He went sailing and didn’t return for a long, long timeMany years later, the boy returned .”Sorry, but I don’t have anything for you anymore ,” the tree said, crying.“All I need is a place to rest. I am tired after my travels.”The tree replied,”Good ! Old tree roots(根) are the best place to rest.” The boy sat down and the tree was glad.The tree in this story is like your parents. Your parents are reliable and giving, like a tree, and will always love you, no matter where you are.【1】Did the boy play around the big tree when he grew up?【2】How did the boy get the money?【3】What did the boy use the branches for?【4】How did the boy feel the last time he returned to the tree?【5】What does the write compare the tree to?