設(shè)函數(shù)
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,
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,則
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的最大值為____________,最小值為___________.
解:因為y’=lnx+1,則當x
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,函數(shù)先減后增,則利用函數(shù)的單調(diào)性可知函數(shù)的最大值為e,最小值為
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知函數(shù)
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(
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).
(1)若
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,求函數(shù)
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的極值;
(2)若
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在
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內(nèi)為單調(diào)增函數(shù),求實數(shù)a的取值范圍;
(3)對于
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,求證:
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)
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的導(dǎo)數(shù)
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滿足
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,其中
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.
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求曲線
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在點
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處的切線方程;
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設(shè)
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,求函數(shù)
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的極值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(12分)設(shè)函數(shù)
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在
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及
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時取得極值.
(Ⅰ)求a、b的值;
(Ⅱ)若對于任意的
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,都有
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成立,求c的取值范圍.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
對于函數(shù)
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,在使
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成立的所有常數(shù)
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中,我們把
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的最大值
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叫做
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的下確界,則對于
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,且
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不全為
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,
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的下確界是( )
A. | B.2 | C. | D.4 |
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)函數(shù)
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,
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.
(Ⅰ)當
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時,
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取得極值,求
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的值;
(Ⅱ)若
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在
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內(nèi)為增函數(shù),求
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的取值范圍.
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
函數(shù)
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
在
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處有極值
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,那么
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的值分別為
_____ __
_ 。
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
若函數(shù)
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在區(qū)間
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上有最小值,則實數(shù)
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的取值范圍是
.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知函數(shù)

(1) 若
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的一個極值點到直線
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的距離為1,求
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的值;
(2) 求方程
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的根的個數(shù).
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