函数
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图象如图,则函数
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的单调递减区间为( )
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为二次函数,由图得-2,3为极值点。即
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或
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时,
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=0,由韦达定理得:
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,
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函数
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的单调递减区间为
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的为减函数且为正数的范围,是
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科目:高中数学
来源:不详
题型:解答题
已知函数

,①求函数的单调区间;②求函数的极值,③当

时,求函数的最大值与最小值.
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科目:高中数学
来源:不详
题型:解答题
已知函数

,当

时,函数

取得极大值.
(1)求实数

的值;
(2)已知结论:若函数

在区间

内导数都存在,且

,则存在

,使得
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.试用这个结论证明:若

,函数

,则对任意

,都有
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;
(3)已知正数

,满足
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,求证:当
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,
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时,对任意大于
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,且互不相等的实数

,都有
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
.
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科目:高中数学
来源:不详
题型:单选题
设函数

则

( )
A在区间

内均有零点。
B在区间

内均无零点。
C在区间

内有零点,在区间

内无零点。
D在区间

内无零点,在区间

内有零点。
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科目:高中数学
来源:不详
题型:解答题
设函数
(1)当

时,求函数

的最大值;
(2)令

,(

)其图象上任意一点

处切线的斜率
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≤

恒成立,求实数

的取值范围;
(3)当

,

,方程
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有唯一实数解,求正数

的值.
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科目:高中数学
来源:不详
题型:填空题
设

的导函数

满足

,其中常数

,则曲线
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在点
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处的切线方程为
。
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科目:高中数学
来源:不详
题型:解答题
已知函数

,曲线
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在点

处的切线为

,若
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时,
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有极值.
(1)求

的值;
(2)求

在

上的最大值和最小值.
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科目:高中数学
来源:不详
题型:单选题
若函数f(x)=x
3-3x在(a,6-a
2)上有最小值,则实数a的取值范围是( )
A.(- ,1) | B.[- ,1) |
C.[-2,1) | D.(-2,1) |
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