作者Insomniac (Insomniac)
看板Math
标题Re: [分析] 两题高微
时间Sat Feb 19 23:45:26 2011
※ 引述《Jer1983 (stanley)》之铭言：
: 1.
: let f:[a,b] -> R be a differentialble function. f'(a) = +infinity
: f'(b) = -infinity. For c in R, there exists x and y in [a,b]
: such that f'(x) > c and f'(y) < c. 请问这件事是怎麽做到的?
我想题目应该是there exists x and y in (a,b) such that....
If not, then there exists c such that |f'(x)| < c for all x in (a,b)
By mean value theorem, |(f(x)-f(a))/(x-a)|=|f'(d)|< c for some d in (a,b)
Let x goes to a, then f'(a) is bounded.
: 2.
: let f:(a,b) -> R be a differentiable function, then |f(x)| <= K for
: x in (a,b). 请问这边是怎麽来的? (我只知道连续函数在闭区间是有界)
这是错的, f(x)=1/x in (0,1) 就是反例
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 69.223.185.63
1F：推 Jer1983 :请问第二题 |f'(x)| 会是有界吗? 02/20 00:08
2F：→ Jer1983 :其实这是李杰高微里面的一个题目 我怀疑打错了 02/20 00:08
3F：推 silvermare :f(x)=log(x) 02/20 01:55