作者t0127754 (阿彥)
看板trans_math
標題[微分] 不等式
時間Tue Jul 8 00:00:01 2008
Let f be a real-valued differentiable function on R
s.t f'(x)>f(x) for all real number x.
Assume that f(0)=0 show that f(x)>0 for all x >0
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◆ From: 118.169.48.173
1F：推 LeoRen:若f(x)>0 => f'(x)/f(x) >1 => lnf(x)>x118.161.144.169 07/08 01:27
2F：→ LeoRen:=> f(x)>e^x, f(0)>1 矛盾!118.161.144.169 07/08 01:28
3F：→ LeoRen:lnf(x)>x+c =>f(x)>exp(x+c),f(0)>0 矛盾118.161.144.169 07/08 01:34
4F：→ t0127754:所以題目錯了? 118.169.48.173 07/08 01:38
5F：→ t0127754:不對阿 那是不定積分 要加常數C 才會對 118.169.48.173 07/08 01:39
6F：→ t0127754:應該沒有矛盾吧 118.169.48.173 07/08 01:40
7F：→ LeoRen:看我所舉的反例是否無誤,若是那題目就有誤118.161.144.169 07/08 01:42
8F：→ LeoRen:第3行便是118.161.144.169 07/08 01:43
9F：→ LeoRen:第2行是c=0的特例118.161.144.169 07/08 01:44
10F：推 Dazaiosamu:科218.174.107.186 07/08 20:56