> For the complete documentation index, see [llms.txt](https://jaydenyl.gitbook.io/diary/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaydenyl.gitbook.io/diary/2020/june/06-18-thu.md).

# 06-18 THU

这几天在读《对倒》（刘以鬯），我读书好像没什么计划，想读就读，有时候觉得无趣就放下了，以前的计划已没有严格执行，但压力却小了很多，不知是好是坏。

有空去看看王家卫的《花样年华》，他们说王家卫的灵感来自于《对倒》，可能是个中年人才能读懂其中的细腻与矜持吧，但我还是想去看看。

“ 如果多一张船票，你会不会跟我走？“

今日份心血来潮LATEX

![answer](https://i.loli.net/2020/06/18/rzLqDT6Siu9I4FZ.png)

## ***附***

***LATEX源码:***

```
###1.
​
**已知  $ f(x) = \frac{2^x}{1+a\cdot2^x} $  关于点$（0，1）$  对称，求   $ a = \_\_$**
​
​
​
***解：***
​
$f(x)$ 关于点 $（0，1）$ 对称，则有：  $ f(-1) + f(0) = 2f(0)$
​
$\frac{2}{1+2a} + \frac{\frac{1}{2}}{1+\frac{1}{2}a} = 2\times\frac{1}{1+a}$
​
得： $a = \frac{1}{2} $
​
​
​
### 2.
​
已知关于  $x$  的函数  $y = a^{2x} + 2a^x -1$ 在 区间 $[-1,1]$  的最值为 $14$ , 求  $a$  的值。
​
​
​
***解：*** 
​
令 $a^x = t $  ，则  $f(t) = t^2 + 2t -1$  , 在 $[-1, \infty)$ 上递增
​
  ####  (1）
​
• 当  $a \in (0,1)$  时，$t \in [a, \frac{1}{a}]$  , $f(t)$ 在 $t = \frac{1}{a}$  时有最大值 $14$ , 代入得：
​
• $(\frac{1}{a})^2 + \frac{2}{a} -1 = 14$
​
• 解之得： $a_1 = \frac{1}{3} $ ，   $a_2= -\frac{1}{5} \notin [-1, 1]$  
​
  ####  (2)
​
• 当  $a \in [1, +\infty)$ 时，$t \in [\frac{1}{a}, a]$ ，$f(t)$在  $t = a$ 时有最大值 $14$ 代入得：
​
• $a^2 + 2a -1 = 14$
​
• 解之得 ：$ a_1 = 3$   $a_2 = -5 \notin [-1, +\infty)$
​
综上所述， $a = 3 $  或  $ \frac{1}{3}$ 
​
​
```


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