(本題滿分12分)已知函數(shù)

在R上是減函數(shù),求實數(shù)

的取值范圍。
a

-3。
試題分析:f′(x)=

,由已知


0在R上恒成立。
當(dāng)a=0時,6x-1

0,得x


,在R上不恒成立。
當(dāng)a

0時,要使得f′(x)

0在R上恒成立,須滿足a<0且△

0,
解得a

-3,故當(dāng)a

-3時,函數(shù)

在R上是減函數(shù).
點評:若


恒成立


;若


恒成立


。此題中沒有限制二次項系數(shù)不為零,所以不要忘記討論。
練習(xí)冊系列答案
相關(guān)習(xí)題
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分10分)
已知函數(shù)

(1)解關(guān)于

的不等式

;
(2)若函數(shù)

的圖象恒在函數(shù)

圖象的上方,求

的取值范圍。
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
設(shè)

,則

的大小關(guān)系是
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分10分)【選修4—5:不等式選講】
設(shè)函數(shù)

(I)畫出函數(shù)

的圖象;
(II)若關(guān)于

的不等式

有解,求實數(shù)

的取值范圍.
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(12分)若

,證明:

查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知

,并且

是方程

的兩根

則實數(shù)

的大小關(guān)系是
查看答案和解析>>
科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
已知正實數(shù)a,b滿足

則使

恒成立的實數(shù)

的取值范圍
查看答案和解析>>