【題目】. 已知函數(shù)（為自然對(duì)數(shù)的底數(shù)）有兩個(gè)極值點(diǎn)，則實(shí)數(shù)的取值范圍是（ ）

A. B. C. D.

【答案】A

【解析】 ，

若函數(shù)有兩個(gè)極值點(diǎn)，

則 和 在 有 2 個(gè)交點(diǎn)，

令 , 則 ，

在遞減 , 而 ，

故 時(shí) , , 即, 遞增，

時(shí) , , 即,遞減，

故，

而 時(shí) , ,時(shí) , ，

若 和 在 有 2 個(gè)交點(diǎn)

只需 ，

點(diǎn)晴：本題考查函數(shù)導(dǎo)數(shù)與函數(shù)的極值點(diǎn)的個(gè)數(shù)問(wèn)題：可利用數(shù)形結(jié)合的辦法判斷交點(diǎn)個(gè)數(shù)，如果函數(shù)較為復(fù)雜，可結(jié)合導(dǎo)數(shù)知識(shí)確定極值點(diǎn)和單調(diào)區(qū)間從而確定其大致圖象.方程的有解問(wèn)題就是判斷是否存在零點(diǎn)的問(wèn)題，可參變分離，轉(zhuǎn)化為求函數(shù)的值域問(wèn)題處理. 恒成立問(wèn)題以及可轉(zhuǎn)化為恒成立問(wèn)題的問(wèn)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(lái)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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