解题方法
1 . 已知函数
.
(1)当a=2时,试判断
在
上的单调性,并证明;
(2)若
时,
是减函数,
时,
是增函数,试求a的值及
上
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee15664d5a8e127810c71f4e5d33214.png)
(1)当a=2时,试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce2594833690eedb3328fe747feb3a3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce2594833690eedb3328fe747feb3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce2594833690eedb3328fe747feb3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2 . 已知函数f(x)=ax2-2ax+1+b(a>0)在区间[2,3]上有最大值4和最小值1.
(1)求a,b的值;
(2)设g(x)=f(x)+log4(4x+1)-x2-1,证明:对任意实数k,函数y=g(x)的图象与直线y=-3x+k最多只有一个交点.
(1)求a,b的值;
(2)设g(x)=f(x)+log4(4x+1)-x2-1,证明:对任意实数k,函数y=g(x)的图象与直线y=-3x+k最多只有一个交点.
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名校
3 . 已知函数
是奇函数.
(Ⅰ)设
,用函数单调性的定义证明:函数
在区间
上单调递减;
(Ⅱ)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121f298b6b225276cc6239079a45606e.png)
(Ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228496ed9aa8365b59805fdb47b1da44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc30165c18de623d0a3efb961e606d1c.png)
(Ⅱ)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c45e65471ae443c9847731fc016e3f.png)
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11-12高一上·吉林·期末
解题方法
4 . 设
为奇函数,
为常数.
(1)求
的值;
(2)证明:
在(1,+∞)内单调递增;
(3)若对于[3,4]上的每一个
的值,不等式
恒成立,求实数
的取值范围.
![](https://img.xkw.com/dksih/QBM/2012/1/30/1578138448928768/1578138449518592/STEM/c877da4c937749d383df4f591787ec16.png)
![](https://img.xkw.com/dksih/QBM/2012/1/30/1578138448928768/1578138449518592/STEM/f39af48f7ebe4ced953935808f137b22.png)
(1)求
![](https://img.xkw.com/dksih/QBM/2012/1/30/1578138448928768/1578138449518592/STEM/f39af48f7ebe4ced953935808f137b22.png)
(2)证明:
![](https://img.xkw.com/dksih/QBM/2012/1/30/1578138448928768/1578138449518592/STEM/70ff443b4bc54c1db42c9384969c1d7a.png)
(3)若对于[3,4]上的每一个
![](https://img.xkw.com/dksih/QBM/2012/1/30/1578138448928768/1578138449518592/STEM/644d1e62239349598267c2af3b36be09.png)
![](https://img.xkw.com/dksih/QBM/2012/1/30/1578138448928768/1578138449518592/STEM/094454a0f086498ba08414d5cc6ecb9f.png)
![](https://img.xkw.com/dksih/QBM/2012/1/30/1578138448928768/1578138449518592/STEM/6c4577d458234d7397784b59447bd85d.png)
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