Question

設(shè)函數(shù)f(x)在R上可導(dǎo),其導(dǎo)函數(shù)為f ^/(x),且函數(shù)y = (1−x) f ^/(x)的圖像如圖所示,則下列結(jié)論中一定成立的是

A．函數(shù)f(x)有極大值f(2)和極小值f(1)          

B．函數(shù)f(x)有極大值f(−2)和極小值f(1)       

C．函數(shù)f(x)有極大值f(2)和極小值f(−2)             

D．函數(shù)f(x)有極大值f(−2)和極小值f(2)

 

Answer 1

【答案】

D

【解析】

試題分析：由y = (1−x) f ^/(x)的圖像得當(dāng)

據(jù)此可知函數(shù)f(x)有極大值f(−2)和極小值f(2).

考點(diǎn)：本小題考查了函數(shù)的導(dǎo)數(shù)與極值的關(guān)系,以及函數(shù)的圖像等內(nèi)容.

點(diǎn)評(píng)：本小題應(yīng)從分析y = (1−x) f ^/(x)的圖像入手，確定導(dǎo)數(shù)正負(fù)時(shí)對(duì)應(yīng)的x的取值區(qū)間，再根據(jù)極值點(diǎn)左正右負(fù)為極大值，極值點(diǎn)左負(fù)右正為極小值.