+_+*
来源:学生作业帮 编辑:拍题作业网作业帮 分类:数学作业 时间:2024/06/17 22:21:39
老师,这题怎么做,谢谢
![](http://img.wesiedu.com/upload/7/34/7349d5bf99483846e93f04d67d9236ff.jpg)
![](http://img.wesiedu.com/upload/7/34/7349d5bf99483846e93f04d67d9236ff.jpg)
解题思路: 函数 。。
解题过程:
解:(1)当a=6时,∵x∈[1,6],∴f(x)=a-x-
+a=2a-x-
;任取x1,x2∈[1,6],且x1<x2,
则f(x1)-f(x2)=(2a-x1-
)-(2a-x2-
)=(x2-x1)+(
-
)=(x2-x1)•
,
当1≤x1<x2<3时,x2-x1>0,1<x1x2<9,∴f(x1)-f(x2)<0,即f(x1)<f(x2),∴f(x)是增函数,增区间是[1,3);
当3≤x1<x2≤6时,x2-x1>0,x1x2>9,∴f(x1)-f(x2)>0,即f(x1)>f(x2),∴f(x)是减函数,减区间是[3,6];
(2)∵a∈(1,6),∴f(x)=
,
①当1<a≤3时,f(x)在[1,a]上是增函数,在[a,6]上也是增函数,
∴当x=6时,f(x)取得最大值
.
②当3<a<6时,f(x)在[1,3]上是增函数,在[3,a]上是减函数,在[a,6]上是增函数,
而f(3)=2a-6,f(6)=
,
当3<a≤
时,2a-6≤
,当x=6时,f(x)取得最大值为
.
当
≤a<6时,2a-6>
,当x=3时,f(x)取得最大值为2a-6.
综上得,M(a)=
.
解题过程:
解:(1)当a=6时,∵x∈[1,6],∴f(x)=a-x-
![](http://img.wesiedu.com/upload/e/7f/e7fc2ef6ba01392ce88b4fe87badee94.png)
![](http://img.wesiedu.com/upload/e/67/e673467ecddf842db3888a16b724141c.png)
则f(x1)-f(x2)=(2a-x1-
![](http://img.wesiedu.com/upload/2/1f/21f2d8f0efe187a1cfe2de8685756034.png)
![](http://img.wesiedu.com/upload/8/76/876aec3f15a2fff8b4121c5bfe8112fe.png)
![](http://img.wesiedu.com/upload/5/a2/5a285e8c64c89aa4459a5546ca56b7de.png)
![](http://img.wesiedu.com/upload/2/0d/20de7c5f99d30b7deb2f307c8de00b38.png)
![](http://img.wesiedu.com/upload/7/0f/70fd7a12071a7939e39e793ced4492ac.png)
当1≤x1<x2<3时,x2-x1>0,1<x1x2<9,∴f(x1)-f(x2)<0,即f(x1)<f(x2),∴f(x)是增函数,增区间是[1,3);
当3≤x1<x2≤6时,x2-x1>0,x1x2>9,∴f(x1)-f(x2)>0,即f(x1)>f(x2),∴f(x)是减函数,减区间是[3,6];
(2)∵a∈(1,6),∴f(x)=
![](http://img.wesiedu.com/upload/b/09/b09366fb052db4a008b08a6af20e9a1b.png)
①当1<a≤3时,f(x)在[1,a]上是增函数,在[a,6]上也是增函数,
∴当x=6时,f(x)取得最大值
![](http://img.wesiedu.com/upload/5/f6/5f644137c757f0a579c0e797c317377b.png)
②当3<a<6时,f(x)在[1,3]上是增函数,在[3,a]上是减函数,在[a,6]上是增函数,
而f(3)=2a-6,f(6)=
![](http://img.wesiedu.com/upload/9/ac/9ac815196030a50c5e9129517db0430b.png)
当3<a≤
![](http://img.wesiedu.com/upload/b/13/b13ffcfd293aef4da5674a4da8175271.png)
![](http://img.wesiedu.com/upload/f/81/f818bf474d7a98c38b798ddf1e1e3e75.png)
![](http://img.wesiedu.com/upload/9/79/979b4be5c57ab1485493c235f23d42ce.png)
当
![](http://img.wesiedu.com/upload/f/01/f012d62a63d3206aa64af637f2aeec84.png)
![](http://img.wesiedu.com/upload/b/52/b52efd21401bc20e1d427527e1a70f52.png)
综上得,M(a)=
![](http://img.wesiedu.com/upload/6/46/6469cd2c6d5de96a1f43a6abcd4a7b49.png)