-
设函数f(x)=ax3-2bx2+cx+4d (a、b、c、d∈R)图象关于原点对称,且x=1时,f(x)取极小值-
.
(1)求a、b、c、d的值;
(2)当x∈[-1,1]时,图象上是否存在两点,使得过此两点处的切线互相垂直?证明你的结论;
(3)若x1,x2∈[-1,1]时,求证:|f(x1)-f(x2)|≤
.
-
设函数f(x)=ax3-2bx2+cx+4d (a、b、c、d∈R)图象关于原点对称,且x=1时,f(x)取极小值-
.
(1)求a、b、c、d的值;
(2)当x∈[-1,1]时,图象上是否存在两点,使得过此两点处的切线互相垂直?证明你的结论;
(3)若x1,x2∈[-1,1]时,求证:|f(x1)-f(x2)|≤
.
-
设函数f(x)=ax3-2bx2+cx+4d(a,b,c,d∈R)的图象关于原点对称,且x=1时,f(x)取极小值
.
(1)求a,b,c,d的值;
(2)若x1,x2∈[-1,1]时,求证:
.
-
已知函数f(x)=ax3+bx2+cx+d(a≠0),图象关于原点对称,且当x=
时,f(x)的极小值为-1,求f(x)的解析式.
-
已知函数f(x)=ax3+bx2+cx+d(a,b,c,d∈R),且函数f(x)的图象关于原点
对称,其图象在x=3处的切线方程为8x-y-18=0
(1)求f(x)的解析式;
(2)是否存在区间[m,n],使得函数g(x)的定义域和值域均为[m,n],且其解析式为f(x)的解析式?若存在,求出这样一个区间[m,n];若不存在,则说明理由.
-
已知函数f(x)=ax3+bx2+cx,其导函数y=f′(x)的图象经过点(1,0),(2,0),如图所示,则下列说法中正确结论的序号为________.
①当x=
时函数取得极小值;
②f(x)有两个极值点;
③当x=2时函数取得极小值;
④当x=1时函数取得极大值.
-
已知函数f (x)=ax3+bx2+cx,其导函数y=f ′(x)的图象经过点(1,0),(2,0),如图所示,则下列说法中不正确的序号是________.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGMAAABaCAYAAACsTujwAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAc6SURBVHhe7ZxZSFVdFMd7LujtezToocDHaCSI
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CGFBK5K1G1fNFH4pmhYE9wYPHqxqSyhuaoYTmHOMHj2aVfSgORo1apSYjPdIcWUGwGbJCxcusAqn
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Or9oQK2SejRGW4g0AyDi6Tbr8OjRo+KXVltDrBnIcXIbIhk2bJio3atuEWsGwIgIkdZIcPOzUhFt
BkhNTW1zhQwTLMzeYx3xZiBJGfGdwN/Jd8L5+PEjDR8+/K8JaCwi3gyAnCenHCuEqCdMmOB5tNcU
MWEGwKwfIY79+/erFE3kQKWlpbUYDYhFYsYMgJHSpk2bVKgdayFeRXilEFNm/NexZgjCmiEIa4Yg
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CWikrLGtiwAAAABJRU5ErkJggg==
)
①当x=
时函数取得极小值;②f(x)有两个极值点;
③当x=2时函数取得极小值;④当x=1时函数取得极大值.
-
已知函数f (x)=ax3+bx2+cx,其导函数y=f ′(x)的图象经过点(1,0),(2,0),如图所示,则下列说法中不正确的序号是________.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGMAAABaCAYAAACsTujwAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAc6SURBVHhe7ZxZSFVdFMd7LujtezToocDHaCSI
XhL0e7AeQrCyoslGm2xQbM7mHhooywbKTG2gIi3TiEiwgWimOaJJzSYbDLNhdf+7dePeOuo913P2
Xvf79g82nf85Yt7zv3tae+3d4cePH/8ESpIt5ksHIhoSKBYBoGb8y9cWw3huxrVr1/jK4hZPzaip
qaGhQ4eysrjFUzNOnz5NnTp1onfv3vEdolu3blFDQ4O6vnPnjvrX4oynZixevJg6duxIp06dUvrS
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09ON9xsPHz6kWbNmsZKDdjPmzp1Lt2/fZmWGffv2qQmfNLSbkZ+fT4WFhazMMH/+fDGR2lC0m4Hd
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CWikrLGtiwAAAABJRU5ErkJggg==
)
①当x=
时函数取得极小值;②f(x)有两个极值点;
③当x=2时函数取得极小值;④当x=1时函数取得极大值.
-
已知函数f (x)=ax3+bx2+cx,其导函数y=f ′(x)的图象经过点(1,0),(2,0),如图所示,则下列说法中不正确的序号是________.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGMAAABaCAYAAACsTujwAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAc6SURBVHhe7ZxZSFVdFMd7LujtezToocDHaCSI
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CWikrLGtiwAAAABJRU5ErkJggg==
)
①当x=
时函数取得极小值;②f(x)有两个极值点;
③当x=2时函数取得极小值;④当x=1时函数取得极大值.
-
![](https://img.xintiku.com/upload/97/98/97988887bd798787a3cb5c356f605755.png)
设f(x)=ax3+bx2+cx的极小值为-8,其导函数y=f'(x)的图象经过点
,如图所示,
(1)求f(x)的解析式;
(2)若对x∈[-3,3]都有f(x)≥m2-14m恒成立,求实数m的取值范围.