已知

在區(qū)間

上是增函數(shù).
(1)求實數(shù)

的值組成的集合

;
(2)設關于

的方程

的兩個非零實根為

、

.試問:是否存在實數(shù)

,使得不等式

對任意

及

恒成立?若存在,求

的取值范圍;若不存在,請說明理由.
(1)實數(shù)a的值組成的集合

;
(2)存在實數(shù)

,使得不等式

對任意

及

恒成立.
試題分析:(1)先求出函數(shù)

的導數(shù)

,將條件

在區(qū)間

上為增函數(shù)這一條件轉化為

在區(qū)間

上恒成立,結合二次函數(shù)的圖象得到

,從而解出實數(shù)

的取值范圍;(2)先將方程

轉化為一元二次方程,結合韋達定理得到

與

,然后利用


將

用參數(shù)

進行表示,進而得到不等式

對任意

及

恒成立,等價轉化為

對任意

恒成立,將不等式

轉化為以

為自變量的一次函數(shù)不等式恒成立,只需考慮相應的端點值即可,從而解出參數(shù)

的取值范圍.
試題解析:(1)因為

在區(qū)間

上是增函數(shù),
所以,

在區(qū)間

上恒成立,

,
所以,實數(shù)

的值組成的集合

;
(2)由

得

,即

,
因為方程

,即

的兩個非零實根為

、

,

、

是方程

兩個非零實根,于是

,

,

,

,

,
設

,

,
則

,
若

對任意

及

恒成立,
則

,解得

或

,
因此,存在實數(shù)

或

,使得不等式

對任意

及

恒成立.
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
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
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
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
,
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
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
;
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
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
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
cos

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
,

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
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
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
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
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
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
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
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,
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的圖像與直線
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的兩個相鄰交點的距離等于
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,則
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的單調(diào)遞增區(qū)間是( )
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