【題目】. 已知函數(shù)（為自然對數(shù)的底數(shù)）有兩個極值點，則實數(shù)的取值范圍是（ ）

A. B. C. D.

【答案】A

【解析】 ，

若函數(shù)有兩個極值點，

則 和 在 有 2 個交點，

令 , 則 ，

在遞減 , 而 ，

故 時 , , 即, 遞增，

時 , , 即,遞減，

故，

而 時 , ,時 , ，

若 和 在 有 2 個交點

只需 ，

點晴：本題考查函數(shù)導(dǎo)數(shù)與函數(shù)的極值點的個數(shù)問題：可利用數(shù)形結(jié)合的辦法判斷交點個數(shù)，如果函數(shù)較為復(fù)雜，可結(jié)合導(dǎo)數(shù)知識確定極值點和單調(diào)區(qū)間從而確定其大致圖象.方程的有解問題就是判斷是否存在零點的問題，可參變分離，轉(zhuǎn)化為求函數(shù)的值域問題處理. 恒成立問題以及可轉(zhuǎn)化為恒成立問題的問題，往往可利用參變分離的方法，轉(zhuǎn)化為求函數(shù)最值處理．也可構(gòu)造新函數(shù)然后利用導(dǎo)數(shù)來求解.注意利用數(shù)形結(jié)合的數(shù)學(xué)思想方法.

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