已知函数
,若对任意
,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/792ba26069c0c4d55702eeb18b7b0e4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48aac90cfacaf530d291001e52b653c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55cbb4a745fc1e5d8db44d5c126eadd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
更新时间:2020-07-27 08:21:16
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解题方法
【推荐1】已知函数f(x)=
ax3-
bx2+x(a,b∈R).
(1)当a=2,b=3时,求函数f(x)极值;
(2)设b=a+1,当0≤a≤1时,对任意x∈[0,2],都有m≥|f′(x)|恒成立,求m的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)当a=2,b=3时,求函数f(x)极值;
(2)设b=a+1,当0≤a≤1时,对任意x∈[0,2],都有m≥|f′(x)|恒成立,求m的最小值.
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适中
(0.65)
【推荐2】已知抛物线
,点A
,B
,抛物线上的点P(x0,y0)
.
(1)求直线AP斜率的取值范围;
(2)Q是以AB为直径的圆上一点,且
·
=0,求
·
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ad7c068b9b7c0fd764cf7746407079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3daebe1e374be642316c6e5424a28e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b51845b16080dba234153476cd6122f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74431786013c0ff1dff20b3af0d5df96.png)
(1)求直线AP斜率的取值范围;
(2)Q是以AB为直径的圆上一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1395fa3420959a18d91b324adc622116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754ddf1a5ca7574269843d1c73caf6f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1395fa3420959a18d91b324adc622116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d52a30af7c4d2ddf0137524d466ad14.png)
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适中
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【推荐1】已知函数
,函数
.
(1)求函数
的单调区间;
(2)若对任意
,函数
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44564eeb6c76f0bc4d4799f914c5f44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c489c1b6d4840f399f0398b7af4169d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df52ede9e310a5c53ba483c732c11626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdda91b3f668548adb7ea3b66759f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
【推荐2】已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b39cd9c40fb254341b3e910829898de.png)
(1)判断
的零点个数;
(2)若
对任意
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b39cd9c40fb254341b3e910829898de.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d764d01af62f15ec7592a12612392563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐3】设函数
.
(1)函数
在区间
是单调函数,求实数
的取值范围;
(2)若存在
,使得
成立,求满足条件的最大整数
;
(3)如果对任意的
都有
成立,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c9a1350ea5666422a66655d4a2f2af.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98eea3f094fa9f139a2e19753f6a1418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f307e1b42f0604a588807bd4852be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)如果对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de1897b8303b5221cde0e7327a4ba25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a4596401432faab4d2593f619719e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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