Question

設函數(shù)f(x)在R上可導,其導函數(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

D

解析試題分析：由y=(1?x) f^/(x)的圖像得當
據(jù)此可知函數(shù)f(x)有極大值f(?2)和極小值f(2).
考點：本小題考查了函數(shù)的導數(shù)與極值的關系,以及函數(shù)的圖像等內容.
點評：本小題應從分析y=(1?x) f^/(x)的圖像入手，確定導數(shù)正負時對應的x的取值區(qū)間，再根據(jù)極值點左正右負為極大值，極值點左負右正為極小值.