【題目】【2017高考課標2 文21】設函數
.
（1）討論
的單調性；
（2）當
時，
，求
的取值范圍.
【答案】（Ⅰ）在
和
單調遞減，在
單調遞增（Ⅱ）
【解析】
試題分析：（1）先求函數導數，再求導函數零點，列表分析導函數符號確定單調區間（2）對
分類討論，當a≥1時，
，滿足條件；當
時，取
，當0＜a＜1時，取
，
.
試題解析：（1）
令
得
當
時，
；當
時，
；當
時，
所以
在 和單調遞減，在單調遞增
(2) 
當a≥1時，設函數h(x)=（1-x）ex，h’(x)= -xex＜0（x＞0），因此h(x)在[0，+∞)單調遞減，而h(0)=1，
故h(x)≤1，所以
f(x)=（x+1）h(x)≤x+1≤ax+1
當0＜a＜1時，設函數g（x）=ex-x-1，g’（x）=ex-1＞0（x＞0），所以g（x）在在[0，+∞)單調遞增，而g(0)=0，故ex≥x+1
當0＜x＜1，
，
，取
則
當時，取
綜上，a的取值范圍[1，+∞）
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瑯嬛福地記
【明】張岱
晉太康中，張茂先①為建安從事，游于洞山。緣溪深入，有老人枕書石上臥，茂先坐與論說。視其所枕書，皆蝌蚪文，莫能辨，茂先異之。老人問茂先曰：“君讀書幾何？”茂先曰：“華之未讀者，二十年內書，若二十年外書，則華固已讀盡之矣。”老人微笑，把茂先臂走石壁下，忽有門入，途徑甚寬，至一精舍，藏書萬卷。問老人曰：“何書？”曰：“世史也。”又至一室，藏書愈富。又問：“何書?”老人曰：“萬國志也。”后至一密室，扃鑰甚固，有二黑犬守之，上有署篆，曰“瑯嬛福地”。問老人曰：“何地？”曰：“此玉京、紫微、金真、七瑛、丹書、秘籍。”指二犬曰：“此癡龍也，守此二千年矣。”開門肅茂先入，見所藏書，皆秦漢以前及海外諸國事，多所未聞。如《三墳》《九丘》《連山》《歸藏》《梼杌》《春秋》諸書，亦皆在焉。茂先爽然自失。老人乃出酒果餉之，鮮潔非人世所有。茂先為停信宿而出，謂老人曰：“異日裹糧再訪，縱觀群書。”老人笑不答，送茂先出。甫出，門石忽然自閉。茂先回視之，但見雜草藤蘿，繞石而生，石上苔蘚亦合，初無縫隙。茂先癡
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