(本題10分)已知函數(shù)
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有極值.
(1)求
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的取值范圍;
(2)若
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在
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處取得極值,且當(dāng)
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時,
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恒成立,求
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的取值范圍.
(1)
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(2)
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(1)∵
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,∴
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要使

有極值,則方程
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有兩個實(shí)數(shù)解,
從而△=
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,∴

.
(2)∵

在

處取得極值,
∴

,
∴

.
∴

,
∵

,
∴當(dāng)
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時,
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,函數(shù)單調(diào)遞增,
當(dāng)
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
時,

,函數(shù)單調(diào)遞減.
∴
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時,
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在

處取得最大值

,
∵
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時,
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恒成立,
∴
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
,即

,
∴
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或
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,即

的取值范圍是
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.
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科目:高中數(shù)學(xué)
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
,

.
(1)若

≥4,求
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m>0時,求證

在

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
對于一切

,不等式

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已知函數(shù)

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(1)求實(shí)數(shù)a的值,并判斷

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
滿足

;
(3)在(2)的條件下,
記


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
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
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科目:高中數(shù)學(xué)
來源:不詳
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已知:函數(shù)

(

是常數(shù))是奇函數(shù),且滿足

,
(Ⅰ)求

的值;
(Ⅱ)試判斷函數(shù)

在區(qū)間

上的單調(diào)性并說明理由;
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
在區(qū)間

上的最小值.

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
的定義域?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823132945887289.gif" style="vertical-align:middle;" />,

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
,且對任意正數(shù)

均有

,
(1)判斷函數(shù)

在

上的單調(diào)性;
(2)設(shè)

,比較

與

的大小,并證明你的結(jié)論;
(3)設(shè)

,若

,比較
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與

的大小,并證明你的結(jié)論.
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科目:高中數(shù)學(xué)
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設(shè)

,則

等于( )
A. | B. | C.0 | D.以上都不是 |
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來源:不詳
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已知函數(shù)

的圖象經(jīng)過A(0,1),且在該點(diǎn)處的切線與直線

平行.
(1)求b與c的值;
(2)求

上的最大值與最小值分別為
M(
a),
N(
a),求
F(
a)=
M(
a)-
N(
a)的表達(dá)式.
(3)在)(2)的條件下,當(dāng)a的區(qū)間

上變化時,證明:

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科目:高中數(shù)學(xué)
來源:不詳
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設(shè)函數(shù)

,它們的圖象在
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軸上的公共點(diǎn)處有公切線,則當(dāng)
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時,
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與
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的大小關(guān)系是 ( )
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